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This paper proposes a blind color image watermarking method based on Hadamard transform to deal with the infringement of color images in the complex network environment. First of all, the color watermark image is channeled and each pixel in the channel image is converted into an 8-bit binary code. And then, the color host image is also channeled and expanded into 4 × 4 non-overlapping pixel blocks based on the selected embedding position. Finally, Hadamard transform is put on the pixel block, and 1-bit watermark information is embedded by the coefficient pair of the first line of Hadamard coefficient matrix. When extracting watermark, the watermark can be extracted only by comparing the size relationship of the coefficient pairs without the help of the original image. In this paper, a voting system of the minority obeying the majority is designed and implemented, which actually enhances the robustness of the method. In addition, a high security encryption system is designed by combining symmetric key and public key, and the correlation between RGB color channels is considered. Simulation results show that the proposed method has better robustness, real-time performance and security compared with similar methods, and meets certain requirements in terms of invisibility and capacity. [ABSTRACT FROM AUTHOR]

Raw point cloud (PC) data acquired by 3D sensors or reconstruction algorithms inevitably contain noise and outliers, which can seriously impact downstream tasks, such as surface reconstruction and target detection. To address this problem, this paper proposes an innovative denoising method including the adaptive feature extraction (AFE) module, the gradient field estimation (GFE) module, and the further accelerated gradient ascent (FAGA) module. The method is based on considering the noisy PC as a convolutional distribution of clean PC and noise, and denoising is achieved by updating the positions of the points through gradient ascent iterations. Specifically, for a given noisy PC as input, we first extract global features in the AFE module, which are used as conditions to dynamically guide the extraction of local and non-local features to achieve adaptive feature acquisition. Next, these adaptive features are used as input to the GFE module to estimate the gradient field of the PCs and combined with our proposed FAGA module for denoising operations. Extensive qualitative and quantitative experiments are conducted on synthetic and natural PC datasets, and the results show that the proposed method exhibits superior performance relative to previous state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we first consider the existence conditions, the construction and the enumeration of Hermitian self-dual θ -cyclic and θ -negacyclic codes over I F p 2 , where p is a prime number and θ is the Frobenius automorphism over I F p 2 . We then give necessary and sufficient conditions for the existence of Hermitian self-dual θ -cyclic and θ -negacyclic codes over I F p e where e is an even integer greater than 2. [ABSTRACT FROM AUTHOR]

Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai et al. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is to design codes with sizes as large as possible, such that every codeword can be uniquely reconstructed from any N distinct noisy reads, where N is fixed. In this paper, we study binary reconstruction codes with the constraint that every codeword is balanced, which is a fundamental requirement in the technique of DNA-based storage. For all possible channels with a single edit error and their variants, we design asymptotically optimal balanced reconstruction codes for all N, and show that the number of their redundant symbols decreases from 3 2 log 2 n + O (1) to 1 2 log 2 n + log 2 log 2 n + O (1) , and finally to 1 2 log 2 n + O (1) but with different speeds, where n is the length of the code. Compared with the unbalanced case, our results imply that the balanced property does not reduce the rate of the reconstruction code in the corresponding codebook. [ABSTRACT FROM AUTHOR]

With the rapid development of multimedia technology, considerable achievement has been achieved in image retrieval technology. On the one hand, users' demand for cross-modal retrieval is increasing rapidly. On the other hand, deep hashing algorithms as one of the most prominent high-dimensional reduction methods have received extensive attention. Under such background, the cross-modal retrieval method based on deep hashing came into being. Although the cross-modal hashing learning method has moved a long way in recent years, it still has space of promotion. First, existing cross-modal based hashing algorithms can only map the feature vectors into binary codes with a fixed length. The length of hash codes cannot be modified according to the practical situation. Second, the saturation level of the probability function used in existing methods is too high to concentrate relevant samples very well, which results in low retrieval efficiency. To solve the above problem, a novel variable-length hash code based on adaptive weight was proposed in this paper. The length of hash codes could be adjusted according to the importance of each bit. And a novel probability function based on Cauchy distribution was proposed to generate compact binary codes and make hashing retrieval more efficient. The experiment shows that the proposed cross-modal image retrieval algorithm based on deep hashing outperforms existing related algorithms on the accuracy of retrieval. [ABSTRACT FROM AUTHOR]

Linear codes play a crucial role in various fields of engineering and mathematics, including data storage, communication, cryptography, and combinatorics. Minimal linear codes, a subset of linear codes, are particularly essential for designing effective secret sharing schemes. In this paper, we introduce several classes of minimal binary linear codes by carefully selecting appropriate Boolean functions. These functions belong to a renowned class of Boolean functions, namely, the general Maiorana–McFarland class. We employ a method first proposed by Ding et al. (IEEE Trans Inf Theory 64(10):6536–6545, 2018) to construct minimal codes violating the Ashikhmin–Barg bound (wide minimal codes) by using Krawtchouk polynomials. The lengths, dimensions, and weight distributions of the obtained codes are determined using the Walsh spectrum distribution of the chosen Boolean functions. Our findings demonstrate that a vast majority of the newly constructed codes are wide minimal. Furthermore, our proposed codes exhibit a significantly larger minimum distance, in some cases, compared to some existing similar constructions. Finally, we address this method, based on Krawtchouk polynomials, more generally, and highlight certain generic properties related to it. These general results offer insights into the scope of this approach. [ABSTRACT FROM AUTHOR]

In this paper, δ -dual codes over finite commutative semi-simple rings are defined as a generalization of dual codes over finite commutative semi-simple rings. Some properties of δ -dual codes are given. We present necessary and sufficient conditions for a λ -constacyclic code of length n to be δ -self-dual, δ -self-orthogonal, δ -dual-containing, δ -LCD over finite commutative semi-simple rings. We also study the δ -dual of skew Θ - λ -constacyclic codes over finite commutative semi-simple rings. Among others, we also give necessary and sufficient conditions for a skew Θ - λ -constacyclic code of any length n to be δ -self-dual, δ -self-orthogonal, δ -dual-containing, δ -LCD over finite commutative semi-simple rings. [ABSTRACT FROM AUTHOR]

Biclustering is a two-dimensional data analysis technique, where submatrices of a given data matrix are looked for. Its extension into three-dimensional data is called triclustering. In the paper, a new generalized look into n-dimensional binary data n-clustering is presented. The searching is performed in terms of the Boolean reasoning paradigm, where the original case (the data) is coded into the Boolean formula and its prime implicants are equivalent to the solutions of the original issue. The correctness (finding n-clusters containing only 0s or 1s) and maximality (the n-cluster cannot be expanded in any dimension without the correctness requirement violation) of such an approach have strong mathematical foundations. The paper also shows the application of Boolean reasoning-based n-clustering for small three- and four-dimensional artificial data as well as for some biomedical ones. [ABSTRACT FROM AUTHOR]

The exponential growth of data raises an unprecedented challenge in data analysis: how to retrieve interesting information from such large-scale data. Hash learning is a promising solution to address this challenge, because it may bring many potential advantages, such as extremely high efficiency and low storage cost, after projecting high-dimensional data to compact binary codes. However, traditional hash learning algorithms often suffer from the problem of semantic inconsistency, where images with similar semantic features may have different binary codes. In this paper, we propose a novel end-to-end deep hashing method based on the similarities of binary codes, dubbed CSDH (Code Similarity-based Deep Hashing), for image retrieval. Specifically, it extracts deep features from images to capture semantic information using a pre-trained deep convolutional neural network. Additionally, a hidden and fully connected layer is attached at the end of the deep network to derive hash bits by virtue of an activation function. To preserve the semantic consistency of images, a loss function has been introduced. It takes the label similarities, as well as the Hamming embedding distances, into consideration. By doing so, CSDH can learn more compact and powerful hash codes, which not only can preserve semantic similarity but also have small Hamming distances between similar images. To verify the effectiveness of CSDH, we evaluate CSDH on two public benchmark image collections, i.e., CIFAR-10 and NUS-WIDE, with five classic shallow hashing models and six popular deep hashing ones. The experimental results show that CSDH can achieve competitive performance to the popular deep hashing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we give a classification of extremal Type II Z 4 -codes of length 24. This is equivalent to a classification of 4-frames of the Leech lattice up to the action of the automorphism group. [ABSTRACT FROM AUTHOR]

Global contexts are critical to locating salient objects for salient object detection (SOD). However, the convolution operation in CNNs has a local receptive field, which cannot capture long-distance global information. Recent studies have shown that modernized CNN models with large kernel convolution, such as ConvNeXt, can effectively extend the receptive fields. Based on it, this paper explores the potential of large kernel CNN for SOD task. Inspired by the common information between RGB and depth images in salient objects, we propose a ConvNeXt-based Siamese network with shared weight parameters. This structural design can effectively reduce the number of parameters without sacrificing performance. Furthermore, a depth information preprocessing module is proposed to minimize the impact of low-quality depth images on predicted saliency maps. For cross-modal feature interaction, a dynamic fusion module is designed to enhance cross-modal complementarity dynamically. Extensive experiments and evaluation results on six benchmark datasets demonstrate the outstanding performance of the proposed method against 14 state-of-the-art RGB-D methods. Our code will be released at https://github.com/zyh5119232/CSNet. [ABSTRACT FROM AUTHOR]

In this paper we construct distance-regular graphs admitting a vertex transitive action of the five sporadic simple groups discovered by E. Mathieu, the Mathieu groups M 11 , M 12 , M 22 , M 23 and M 24 . From the binary code spanned by an adjacency matrix of the strongly regular graph with parameters (176,70,18,34) we obtain block designs having the full automorphism groups isomorphic to the Higman-Sims finite simple group. Moreover, from that code we obtain eight 2-designs having the full automorphism group isomorphic to M 22 , whose existence cannot be explained neither by the Assmus-Mattson theorem nor by a transitivity argument. Further, we discuss a possibility of permutation decoding of the codes spanned by adjacency matrices of the graphs constructed and find small PD-sets for some of the codes. [ABSTRACT FROM AUTHOR]

Binary linear codes with few weights have wide applications in communication, secret sharing schemes, authentication codes, association schemes, strongly regular graphs, etc. Projective binary linear codes are among the most important subclasses of binary linear codes for practical applications. In this paper, motivated by the two excellent recent papers (Li et al. in IEEE Trans Inf Theory 67(7):4263–4275, 2021) and (Wang et al. in IEEE Trans Inf Theory 67(8):5133–5148, 2021), several new families of few-weight projective binary linear codes are constructed from the defining sets, and then their Hamming weight distributions are determined by employing the Walsh transform of the corresponding two-to-one functions over finite fields with the even characteristic. Our constructions can produce binary linear codes with new parameters. Some of the constructed binary linear codes are optimal or almost optimal according to the online Database of Grassl, and the duals of some of them are distance-optimal with respect to the sphere packing bound. This paper also shows once again that the two-to-one functions initially studied in (Mesnager and Qu in IEEE Trans Inf Theory 65(12):7884–7895, 2019) are also promising objects in coding theory. Although our derived codes use objects considered in the very recent literature, the analysis of our designed codes involves functions having different algebraic structures (and, therefore, other Walsh transform distribution) and requires solving new systems of equations over finite fields, which is an essential step in determining the weight distribution of our constructed codes. As applications, some of the codes presented in this paper can be used to construct association schemes and secret sharing schemes with interesting access structures. [ABSTRACT FROM AUTHOR]

Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length 2 m - 1 and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in Liu et al (Finite Field Appl 91:102270, 2023). It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated. [ABSTRACT FROM AUTHOR]

Cross-modal hashing which embeds data to binary codes is an efficient tool for retrieving heterogeneous but correlated multimedia data. In real applications, the sizes of queries are much larger than that of the training set and the queries may be dissimilar to training data, which lays bare the shortage of generalization of deterministic models, such as cross-encoder and autoencoder. In this paper, we design a variational cross-encoder (VCE), a generative model, to tackle this problem. At the bottleneck layer, the VCE outputs distributions parameterized by means and variances. As VCE can generate diversified data using noises, the proposed model can perform better in testing data. Ideally, each distribution is expected to describe a category of data and samples of this distribution are expected to generate data in the same category. Under this expectation, the means and variances can be used as real codes for input data. However, the generated data generally are not belonging to the same category as the input data. Hence, we add a penalty term on variance output of VCE and use means as real codes for further generating hashing codes. Experiments on three widely used datasets validate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Because Gray code has good spatial traversal and easy to generate binary conversion, this paper proposes an image encryption algorithm based on Gray code scrambling. Firstly, the Lorenz system is used to generate chaotic sequences for binary and Gray code transformation to achieve global scrambling. Different from the traditional row (column) XOR method, this paper uses the snake shape to diffuse the row (column) XOR. The lines of the scrambled image are first XORed from left to right in a serpentine order, and the row elements are cyclically shifted. Then, the columns of the image are XORed from right to left in a serpentine order, and the column elements are cyclically shifted. Finally, the scrambled image is further diffused. The comparative experiment shows that the algorithm has good encryption effect. Not only is it well resistant to differential cryptanalysis and exhaustive attack, but it also improves key sensitivity. [ABSTRACT FROM AUTHOR]

Background: Bone age assessment assists physicians in evaluating the growth and development of children. However, deep learning methods for bone age estimation do not currently incorporate differential features obtained through comparisons with other bone atlases. Objective: To propose a more accurate method, Delta-Age-Sex-AdaIn (DASA-net), for bone age assessment, this paper combines age and sex distribution through adaptive instance normalization (AdaIN) and style transfer, simulating the process of visually comparing hand images with a standard bone atlas to determine bone age. Materials and methods: The proposed Delta-Age-Sex-AdaIn (DASA-net) consists of four modules: BoneEncoder, Binary code distribution, Delta-Age-Sex-AdaIn, and AgeDecoder. It is compared with state-of-the-art methods on both a public Radiological Society of North America (RSNA) pediatric bone age prediction dataset (14,236 hand radiographs, ranging from 1 to 228 months) and a private bone age prediction dataset from Zigong Fourth People's Hospital (474 hand radiographs, ranging from 12 to 218 months, 268 male). Ablation experiments were designed to demonstrate the necessity of incorporating age distribution and sex distribution. Results: The DASA-net model achieved a lower mean absolute deviation (MAD) of 3.52 months on the RSNA dataset, outperforming other methods such as BoneXpert, Deeplasia, BoNet, and other deep learning based methods. On the private dataset, the DASA-net model obtained a MAD of 3.82 months, which is also superior to other methods. Conclusion: The proposed DASA-net model aided the model's learning of the distinctive characteristics of hand bones of various ages and both sexes by integrating age and sex distribution into style transfer. [ABSTRACT FROM AUTHOR]

Nonlinear optical switching is a prominent technology for high-speed data processing. All-optical switching based on phase-shifted fiber Bragg Grating provides a tremendous opportunity with advantages such as improved efficiency, sensitivity, lightweight, and cost-effective parameters as compared to traditional optical switching for designing different types of optical combinational digital circuits. The paper describes the concepts of phase-shifted FBG structure, which actually, performs the switching on the basis of cross-phase modulation (XPM) scheme and non-linear optics. The paper describes the details of the coupled-mode theory associated with the FBG technology and its effectiveness as a powerful optical switch using the concept of non-linear optics. The non-linear FBG-based switch is analyzed to implement the all-optical 4-bit binary to gray code converter that has been designed. The proposed architecture leads to Very large-scale integration optics (VLSIO), which involves perfect and high-speed switching, switch in fiber(SIF) in the field of all-optical communication systems and switching technology. The proposed scheme can be a stepping stone in the field of fast switching and signal processing and it may provide a new horizon to the switching phenomena. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to study Spanier–Whitehead duality in the K(n)-local category. One of the key players in the K(n)-local category is the Lubin–Tate spectrum E n , whose homotopy groups classify deformations of a formal group law of height n, in the implicit characteristic p. It is known that E n is self-dual up to a shift; however, that does not fully take into account the action of the automorphism group G n of the formal group in question. In this paper we find that the G n -equivariant dual of E n is in fact E n twisted by a sphere with a non-trivial (when n > 1 ) action by G n . This sphere is a dualizing module for the group G n , and we construct and study such an object I G for any compact p-adic analytic group G . If we restrict the action of G on I G to certain type of small subgroups, we identify I G with a specific representation sphere coming from the Lie algebra of G . This is done by a classification of p-complete sphere spectra with an action by an elementary abelian p-group in terms of characteristic classes, and then a specific comparison of the characteristic classes in question. The setup makes the theory quite accessible for computations, as we demonstrate in the later sections of this paper, determining the K(n)-local Spanier–Whitehead duals of E n hH for select choices of p and n and finite subgroups H of G n . [ABSTRACT FROM AUTHOR]

Multiple-input-multiple-output (MIMO) can provide superior performances such as system capacity, linkage, etc. But also it will bring high RF costs and system complexity, especially in large scale MIMO systems. Antenna selection (AS) is proved to be a trade-off between good performances and complexity. Specifically, from the perspective of both transmit and receive antennas, the joint transmit and receive antenna selection (JTRAS) is employed in MIMO systems. Up to now, some algorithms of JTRAS have been studied in MIMO systems. However, most of them are mainly focused on just one aspect about accuracy or complexity. Especially, compared to numerical analysis, the implementation of swarm intelligence algorithm in JTRAS needs to be studied extensively. In the paper, three intelligent algorithms, i.e. genetic algorithm, cat swarm algorithm and particle swarm algorithm are studied and compared in terms of accuracy, cost, and complexity. In addition, fractional coding is proposed in the algorithms instead of binary integer coding. The simulation results demonstrate that all three algorithms can efficiently accomplish the antenna selection. PSO has the best accuracy and stability, but the complexity of PSO is also highest. If we take overall performances in consideration, CSO is the best choice especially in practical implementation. Moreover, fractional coding will provide better performance than binary integer coding. [ABSTRACT FROM AUTHOR]

Multi-view subspace clustering, which partitions multi-view data into their respective underlying subspaces, has achieved the remarkable clustering performance by extracting abundant complementary information from data of different views. However, existing subspace clustering methods almost suffer from very heavy computational burden that restricts their capacity on computational efficiency for large-scale datasets. Recently, hashing/binary code learning has attracted intensive attentions due to fast Hamming distance computation and much less storage requirement, but existing related research does not explore underlying subspace clustering structure well that widely exists in real-world data. In order to handle the both issues, in this paper, we propose a multi-view subspace clustering method named Hashing Multi-view Sparse Subspace Learning (HMSSL). HMSSL incorporates multi-view binary code learning and binary sparse subspace learning with a "thin" dictionary into a unified framework. HMSSL encodes multi-view real-valued features in the original space into compact common binary codes in the Hamming space for fast Hamming distance computation by multi-view binary code learning and learns the binary sparse subspace representation matrix for exploring the underlying subspace clustering structure efficiently and effectively by binary sparse subspace learning with a "thin" dictionary matrix. All the columns of the dictionary matrix are randomly and uniformly sampled from all the columns of the compact common binary code matrix. We design an effective binary optimization algorithm based on alternating direction multiplier method and analyze its time complexity. Extensive experiments performed on six benchmark multi-view datasets demonstrate the effectiveness of HMSSL in comparison with ten state-of-the-art baselines in this field. [ABSTRACT FROM AUTHOR]

In the modern era, smart home technology is considered as the most growing application of Internet of Things (IoT) as they facilitate users for control home devices remotely. Anonymous and efficient authentication approaches in smart home environments are essential for attaining secure communication as the home and user communication channel is highly vulnerable and insecure. In this paper, Merkle Hash Tree and Strongly Constrained Discrete Hashing Function-based Authentication (MHS-SCDHF-AS) that integrates the transaction history and physical context awareness is proposed for enabling security for Smart Home IoT applications. This MHS-SCDHF-AS prevents the problem of clock synchronization and does not utilize a verification table both during the authentication process. This Strongly Constrained Discrete Hashing Functionis a supervised hashing method which overcomes the limitations of large quantization errors and suboptimal binary codes. It is also capable of learning binary codes and significant in resisting the transmission loss as each information used for verification contains its authentication data in itself. The computation cost and communication cost of the proposed MHS-SCDHF-AS is identified to be lesser than the benchmarked authentication schemes considered for investigation. The formal, informal and model checking-based security investigation of the proposed MHS-SCDHF-AS is also confirmed to be superior over the baseline authentication schemes used for smart home environments. [ABSTRACT FROM AUTHOR]

In this paper we prove that the class of Goppa codes whose Goppa polynomial is of the form g (x) = Tr F q m \ F q where Tr F q m \ F q is a trace polynomial from a field extension of degree m ≥ 3 has a better minimum distance than what the Goppa bound d ≥ 2 deg (g (x)) + 1 implies. This result is a significant improvement compared to the minimum distance of Trace Goppa codes over quadratic field extensions (the case m = 2 ). We present two different techniques to improve the minimum distance bound. For general p we prove that the Goppa code C (L , Tr F q m \ F q ) is equivalent to another Goppa code C(M, h) where deg (h) > deg (Tr F q m \ F q ) . For p = 2 we use the fact that the values of Tr F q m \ F q are fixed under q–powers to find several new parity check equations which increase the known distance bounds. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a novel notion of hypergraph-based codes, L.C-hypergraphs and codeable hypergraphs with respect to binary (linear) codes. In order to realize the article's goals, we define the concepts of code-based graphs, consider them as complex networks and construct them from binary (linear) codes via an equivalence relation on (L.C-hypergraphs) codeable hypergraphs. The paper includes implications for the development of fuzzy graph and for modeling the security problems by codeable hypergraphs and applications in complex hypernetworks. The new conception of codeable hypergraphs was given for the first time in this paper. Finally (L.C-hypergraphs), codeable hypergraphs, as complex hypernetworks, are applied as a tool in wireless sensor hypernetworks, code-based graphs, in wireless sensor networks and the bilateral relations between them. [ABSTRACT FROM AUTHOR]

One of the most important functions used in a quantum key distribution (QKD) network is universal hash functions, specially, (almost) strongly universal hash functions which are used in at least three steps of QKD, in particular, in error correction, privacy amplification, and authentication. Also, they have been recently used in several other quantum communication protocols like quantum secret sharing (QSS). These hash functions have also many other important applications from information security to data structures and parallel computing. Recently, Bibak et al. [Quantum Inf. Comput., 2021] introduced quadratic hash which gives much better collision bound than the well-known polynomial hash. In this paper, we define three new universal hash function families which strongly generalize all the previous families and have several advantages over them. Then, using highly influential and pioneering results of Schmidt and of Weil, we show that these new families are (almost) Δ -universal which can then be easily converted to (almost) strongly universal families. This makes them useful for applications in QKD and many other areas. [ABSTRACT FROM AUTHOR]

In this paper, an extended complete LBP (ELBP) for texture classification is proposed, in which the local feature vectors are composed of the ratio of the central pixel and its neighborhood pixels to a specific threshold. ECLBP_C represents the gray level of the image, which is obtained by comparing the center pixel with the global threshold. ECLBP_S and ECLBP_M represent the symbol component and the magnitude component of the 3-neighbor region of the center pixel respectively, which are obtained by calculating two binary codes using the original LBP algorithm for the 3-neighbor region of the center pixel. In order to make the proposed algorithm scalable, in addition to the 3-neighbor pixels of the central pixel, the proposed algorithm use the center pixel as the center, r as the radius in the circle with ɑ as the filter's radius to generate extended binary coding, such as ECLBP_ES_r,α ECLBP_EM_ r,α. In order to describe the local region feature vector in detail, specified ECLBP_ES_r,α and ECLBP_EM_r,α can be obtained by defining the number of extensions according to actual needs, and then established and concatenated all ECLBP gray histograms for statistics. In the experimental part, we analyze the performance of the proposed algorithm in detail, and prove that the algorithm has good scalability and robustness. The experimental results show that the classification accuracy of the proposed algorithm is up to 99% after 3 expansions in Table 2. The source codes of the proposed algorithm can be downloaded from https://github.com/zenqiang/ECLBP.git. [ABSTRACT FROM AUTHOR]

CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes (C 1 , C 2) such that C 1 contains C 2 , C 2 is even, and the shortening of the dual of C 1 with respect to the support of each codeword of C 2 is self-dual. In this paper, we give new conditions to guarantee that a pair of binary codes (C 1 , C 2) is a CSS-T pair. We define the poset of CSS-T pairs and determine the minimal and maximal elements of the poset. We provide a propagation rule for nondegenerate CSS-T codes. We apply some main results to Reed–Muller, cyclic and extended cyclic codes. We characterize CSS-T pairs of cyclic codes in terms of the defining cyclotomic cosets. We find cyclic and extended cyclic codes to obtain quantum codes with better parameters than those in the literature. [ABSTRACT FROM AUTHOR]

The hull of a linear code over finite fields is the intersection of the code and its dual code, which has been widely studied due to its wide applications. In this paper, we develop a general method for constructing linear codes with small hulls using the eigenvalues of the generator matrices. Using this method, we construct many optimal Euclidean and Hermitian LCD codes, which improve the previously known lower bound on the largest minimum distance. We also obtain many (near) MDS LCD codes and (near) MDS codes with one-dimensional hull. Furthermore, we give three tables about formally self-dual LCD codes. [ABSTRACT FROM AUTHOR]

Let C be a four-weight binary code, which has all one vector. Furthermore, we assume that C supports t-designs for all weights obtained from the Assmus–Mattson theorem. We previously showed that t ≤ 5 . In the present paper, we show an analogue of this result in the cases of five and six-weight codes. [ABSTRACT FROM AUTHOR]

Hashing methods have been widely studied in the image research community due to their low storage and fast computation. However, generating compact hash codes is still a challenging task. In this paper, we propose a novel Asymmetric Similarity-Preserving Discrete Hashing (ASPDH) method to learn compact binary codes for image retrieval. Specifically, the pairwise similarity matrix is approximated in the asymmetric learning manner with two different real-valued embeddings. In addition, ASPDH constructs two distinct hash functions from the kernel feature and label consistency embeddings. Therefore, similarity preservation and hash code learning can be simultaneously achieved and interactively optimized, which further improves the discriminative capability of the learned binary codes. Then, a well-designed iterative algorithm is developed to efficiently solve the optimization problem, resulting in high-quality binary codes with reduced quantization errors. Extensive experiments on three public datasets show the rationality and effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we provide a recursive method to construct self-orthogonal and self-dual codes of the type { k 1 , k 2 , ... , k e } and length n over the quasi-Galois ring F 2 r [ u ] / < u e > from a self-orthogonal code of the same length n and dimension k 1 + k 2 + ⋯ + k ⌈ e 2 ⌉ over F 2 r and vice versa, where F 2 r is the finite field of order 2 r , n ≥ 1 , e ≥ 2 are integers, ⌈ e 2 ⌉ is the smallest integer greater than or equal to e 2 , and k 1 , k 2 , ... , k e are non-negative integers satisfying k 1 ≤ n - (k 1 + k 2 + ⋯ + k e) and k i = k e - i + 2 for 2 ≤ i ≤ e. We further apply this recursive method to provide explicit enumeration formulae for self-orthogonal and self-dual codes of an arbitrary length over the ring F 2 r [ u ] / < u e > . With the help of these enumeration formulae and by carrying out computations in the Magma Computational Algebra system, we classify all self-orthogonal and self-dual codes of lengths 2, 3, 4, 5 over the ring F 2 [ u ] / < u 3 > and of lengths 2, 3, 4 over the ring F 4 [ u ] / < u 2 > . [ABSTRACT FROM AUTHOR]

Clustering is a long-standing challenging task in pattern recognition and computer vision. In recent years, with development of multimedia technologies and explosive growth of data, the access to data is various. Clustering data from different feature sources has attracted considerable attentions for the remarkable clustering performance due to exploiting complementary information from data of different features. However, in fact, existing work often suffers from heavy computational load that restricts their capacity for large-scale datasets and most existing methods about fusing multi-view data are not perfect enough, namely, the quality of the joint matrix learned from multiple sources is not high enough. In this paper, we propose an efficient and effective clustering approach which combines sparse subspace learning with a bipartite graph for binary/hash codes produced from data of different sources by a collaborative discrete representation learning model that is an efficient and effective data fusion and binary code learning method. The bipartite graph that owns low time complexity is constructed to extract local geometric structure information for improving clustering performance. Extensive experiments performed on four benchmark datasets validate the efficiency and effectiveness of the proposed approach in comparison with ten state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Unsupervised multi-modal hashing has received considerable attention in large-scale multimedia retrieval areas since its low storage and high search speed. Existing unsupervised multi-modal hashing methods usually aim to mine the complementary information and the structural information for different modalities and preserve them in low-dimensional discrete space. The main limitations are two folds: (1) The shared semantic properties and the specific-modality information between multi-modal data are not explored simultaneously, which limits the improvement of retrieval accuracy. (2) Most multi-modal hashing methods with rough fusion manners cause greatly the information loss. In this paper, we present an unsupervised Joint and Individual Feature Fusion Hashing (JIFFH) that jointly performs the unified feature learning and individual feature learning. A two-layer fusion architecture with an adaptive weighting scheme is adopted to fuse effectively the common semantic properties and the specific-modality data information. The experimental results on three public multi-modal datasets show that our proposed method is better than state-of-the-art unsupervised multi-modal hashing methods. In conclusion, the proposed JIFFH method is very effective to learn discriminative hash codes and can boost retrieval performance. [ABSTRACT FROM AUTHOR]

In the current paper, we study skew cyclic codes over the ring S : = F 2 × (F 2 + v F 2) with v 2 = v . We investigate the structural properties of skew cyclic codes over the ring S . Also, we describe the dual codes of skew cyclic codes with respect to the Euclidean inner product and the Hermitian inner product. Furthermore, we give a necessary and sufficient condition for a skew cyclic code over S to contain its dual. Using these results, we show that binary quantum error-correcting codes as well as entanglement-assisted quantum error-correcting codes can be constructed from skew cyclic codes over S . Finally, we give examples of binary entanglement-assisted quantum error-correcting codes with good parameters from skew cyclic codes over S . [ABSTRACT FROM AUTHOR]

A new road map for design is emerging out of interdisciplinary research across biology and design. Whilst in the second part of the twentieth century, the emergence of the digital realm altered and radically challenged conventional design and manufacturing processes, the beginning of the twenty-first century marks a strong shift towards the amalgamation of the binary code (1s and 0s) with biological systems. With advances in synthetic biology, we can now 'biofabricate' like Nature does. By tinkering and altering the DNA code or the environment of growth of living organisms, we can effectively 'design' and grow new biomaterials. The role of design is shifting from working with inanimate matter such as plastic and metals to making with animate living entities such as mycelium, yeast and bacteria. This paradigm shift promises to open up new possibilities for biofabricating future intelligent materials as well as for engaging with new sustainable processes. This paper examines strategies and tools for designing with living systems and proposes a framework for design to engage with our future bio-materiality. From biofabrication experiments to synthetic biology propositions, the paper will investigate a series of design artifacts that explores strategies such as co-designing with natural organisms or actuating a new synthetic nature and develop a critique of how biodesign can help shifting towards the crafting of a future sustainable intelligent bio-materiality. [ABSTRACT FROM AUTHOR]

Linear codes with complementary dual (LCD codes) play an important role in armoring implementations against side-channel attacks and fault injection attacks. Hermitian LCD codes are a special class of LCD codes, which were proved to be asymptotically good. In this paper, several classes of optimal quaternary Hermitian LCD codes are constructed via constacyclic codes. The binary images of these classes of quaternary Hermitian LCD codes are characterized. Several classes of optimal binary LCD codes with minimum distance 6, and optimal binary linear codes with one-dimensional hull and minimum distance 6 are also presented. [ABSTRACT FROM AUTHOR]

Binary code similarity detection (BCSD) plays a big role in the process of binary application security test. It can be applied in several fields, such as software plagiarism detection, malware analysis, vulnerability detection. Most research is based on recurrent neural networks, which is difficult to get the overall or long-distance semantic information of functions. Besides, exiting works simply extract high-level semantic features, lacking in-depth investigations on the potential mechanisms for fusing low-level and high-level semantic features. In this paper we propose a multi-semantic feature fusion attention network (MFFA-Net) for BCSD. MFFA-Net contains two critical modules: semantic feature fusion (SFF) and attention feature fusion (AFF). The SFF module concatenates multiple semantic features to represent the semantics of the function, which helps to obtain the overall semantic information of the function. The AFF module is designed to find useful information from various features, which assigns an attention matrix to research the relationship between features. In order to evaluate the proposed method, we made extensive experiments on two datasets. MFFA-Net can achieve a high degree of AUC at 99.6% and 98.3% respectively on the two datasets. The experimental results show that MFFA-Net has better performance for BCSD. [ABSTRACT FROM AUTHOR]

In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Hadamard matrix over the k th roots of unity, we can construct a larger Butson matrix over the ℓ th roots of unity for any ℓ dividing k, provided that any prime p dividing k also divides ℓ . We prove that a Z p s -additive code with p a prime number is isomorphic as a group to a BH-code over Z p s and the image of this BH-code under the Gray map is a BH-code over Z p (binary Hadamard code for p = 2 ). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided. [ABSTRACT FROM AUTHOR]

In quantum key distribution (QKD), two users extract a shared secret key using a quantum communication channel in the presence of an eavesdropper. Among QKD protocols, the ones based on energy-time (ET) entanglement of photons have been studied extensively due to their ability to generate high key rates from the arrival times of entangled photons. For the information reconciliation (IR) stage of ET-QKD protocols (where the users communicate using a classical channel in order to reconcile differences in their data), a scheme called multi-level coding (MLC) was proposed by Zhou et al. in prior work. The MLC scheme splits the raw key symbols into bit layers and utilizes binary low-density parity check (LDPC) codes to encode each layer. Although binary LDPC codes are able to offer low complexity decoding for IR, they have poor error-correcting performance compared to their non-binary counterparts, thus leading to low key rates. Additionally, existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this paper, we mitigate the above issues by proposing a flexible protocol for IR in ET-QKD systems called non-binary multi-level coding NB-MLC(a) which is parameterized by a positive integer a. The NB-MLC(a) protocol is a generalization of the MLC scheme and utilizes NB-LDPC codes from a Galois field of size 2 a . We show that by using a small value of a, the NB-MLC(a) protocol significantly improves the key rate without much increase in complexity. To further improve the key rates of the NB-MLC(a) protocol, we propose (i) a joint rate and degree distribution optimization (JRDO) algorithm to design the NB-LDPC codes for the protocol and (ii) an interleaved decoding and communication (IDC) scheme to decode the different layers of the NB-MLC(a) protocol. The JRDO algorithm is designed to use the QKD channel information, and we show that it results in a higher key rate than codes used in prior work. Additionally, the IDC scheme improves the key rate compared to the decoding and communication methods utilized previously in literature. Overall, the NB-MLC(a) protocol that uses JRDO-LDPC codes and the IDC scheme results in a significant 40–60 % improvement in key rates compared to prior work for ET-QKD systems. [ABSTRACT FROM AUTHOR]

Digital data transmission and storage are indispensable components for our contemporary information-driven society. As data volumes keep increasing, the need for efficient coding schemes grows. This paper gives a novel coding scheme for generating sixteen codes from generators with quaternary codes, thereby offering a significant increase in data representation capacity, new possibilities for data encoding and decoding, and an overall improvement in the efficiency of the encoding scheme. This provides up a new perspective for numerous fields that can profit from the proposed scheme, including coding theory, computer science, modeling, and experimental design. We focus on only experimental design and modeling, due to space limits and their importance in designing and modeling real-world and scientific phenomena. The main findings indicate that the new generated sixteen codes can be used as optimal experimental designs with good space-filling behavior when designing large-scale experiments, and as efficient datasets that perform well in fitting various functions even with a small number of points and without modeling assumptions. The relationships between the codewords of the generated sixteen codes and the codewords of the generator quaternary codes are investigated. These relationships provide a benchmark by which to select the generator most efficiently, resulting in codewords that are efficient from multiple angles. Furthermore, the space-filling behavior and isomorphism examination of the sixteen codes generated as designs are deeply theoretically studied. [ABSTRACT FROM AUTHOR]

In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described in Tonchev (J Combinat Theory Ser A 52:197-205, 1989) in order to obtain self-orthogonal codes over an arbitrary field. We extend construction self-orthogonal codes from orbit matrices of self-orthogonal designs and weakly self-orthogonal 1-designs such that block size is odd and block intersection numbers are even described in Crnković (Adv Math Commun 12:607–628, 2018). Also, we generalize mentioned construction in order to obtain self-orthogonal codes over an arbitrary field. We construct weakly self-orthogonal designs invariant under an action of Mathieu group M 11 and, from them, binary self-orthogonal codes. [ABSTRACT FROM AUTHOR]

Let m = 8 k and α be a primitive element of the finite field G F (2 m) , where k ≥ 2 is an integer. In this paper, a class of binary cyclic codes C (u , v) of length 2 m - 1 with two nonzeros α - u and α - v is studied, where (u , v) = (1 , (2 m - 1) / 17) . It turns out that C (u , v) has parameters [ 2 m - 1 , 2 m - m - 9 , 4 ] and is distance-optimal with respect to the Sphere Packing bound. The weight distribution of the dual of C (u , v) is also completely determined based on some results on Gaussian periods. [ABSTRACT FROM AUTHOR]

Steganography is the science of communicating a secret message by hiding it in a cover object. The well known F5 algorithm is based on binary Hamming codes in Hamming graph. It has been an interesting research problem to construct other steganographic schemes from mathematically structured graphs. In this paper, we construct steganographic schemes explicitly from r-perfect codes on Cayley graphs over Gaussian integers, Eisenstein–Jacobi integers, and Lipschitz integers, respectively. Then we further compute various parameters for the suggested steganographic schemes. [ABSTRACT FROM AUTHOR]

In mobile edge computing (MEC) systems, enhancing the learning capabilities of edge nodes through Artificial Intelligence (AI) can improve the efficiency of dynamically allocating resources. For the scenario of edge service migration, various tasks in lightweight IoT devices are offloaded to edge nodes and the services on edge nodes are migrated adaptively to another available node nearer to the users while they move. To speed up network application loading during service migration, this paper proposes an intelligent trace-driven predicting approach (ITPA) that improves the efficiency of I/O scheduling and the hit ratio of caching when migrating services between resource-constrained edge nodes. First, based on the characteristics of sequential access to the binary codes of an application during its startup progress, the request loading list is generated by tracing key I/O requests at that phase. Then, an intelligent algorithm is designed to search and select the key I/O requests in the loading list. Finally, the efficiency of data acquisition is improved by implementing a prefetch strategy for the client side and a three-level caching strategy for the server side. Experimental results show that the ITPA reduces the service startup time during stateless migration. [ABSTRACT FROM AUTHOR]

Code similarity analysis has become more popular due to its significant applicantions, including vulnerability detection, malware detection, and patch analysis. Since the source code of the software is difficult to obtain under most circumstances, binary-level code similarity analysis (BCSA) has been paid much attention to. In recent years, many BCSA studies incorporating AI techniques focus on deriving semantic information from binary functions with code representations such as assembly code, intermediate representations, and control flow graphs to measure the similarity. However, due to the impacts of different compilers, architectures, and obfuscations, binaries compiled from the same source code may vary considerably, which becomes the major obstacle for these works to obtain robust features. In this paper, we propose a solution, named UPPC (Unleashing the Power of Pseudo-code), which leverages the pseudo-code of binary function as input, to address the binary code similarity analysis challenge, since pseudo-code has higher abstraction and is platform-independent compared to binary instructions. UPPC selectively inlines the functions to capture the full function semantics across different compiler optimization levels and uses a deep pyramidal convolutional neural network to obtain the semantic embedding of the function. We evaluated UPPC on a data set containing vulnerabilities and a data set including different architectures (X86, ARM), different optimization options (O0-O3), different compilers (GCC, Clang), and four obfuscation strategies. The experimental results show that the accuracy of UPPC in function search is 33.2% higher than that of existing methods. [ABSTRACT FROM AUTHOR]

This paper defines a new design, simulation and analysis of all-optical analog-to-digital converters (ADC) based on silicon waveguide based all-optical synchronous up counter. The proposed structure consists of a nonlinear magnitude comparator, synchronous up counter and an optical digital to analog converter (DAC). Every proposed counter type ADC module is modelled using silicon optical micro-ring resonator (OMRR) as its core element. The magnitude comparator compares the analog signal to be digitized with the DAC output to generate 4-bit binary codes using a synchronous up counter depending on the evaluation states of the comparator. The digital optical output is detected at the output port of the synchronous up counter circuit numerical simulations authorizing the results with the theoretical results. In addition, the possible configurations of OMRR radius and detuning are specified by analyzing the system performance in terms of the amplitude deviation measure. Furthermore, several performance parameters, including extinction ratio (ER) and on–off ratio, are computed from the simulation outputs attained on MATLAB to evaluate the circuits' accurateness and practicability. [ABSTRACT FROM AUTHOR]

This paper gives new methods of constructing symmetric self-dual codes over a finite field GF(q) where q is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over GF(11), GF(19), and GF(23) of every length less than 42. We also find 153 new self-dual codes up to equivalence: they are [32, 16, 12], [36, 18, 13], and [40, 20, 14] codes over GF(11), [36, 18, 14] and [40, 20, 15] codes over GF(19), and [32, 16, 12], [36, 18, 14], and [40, 20, 15] codes over GF(23). They all have new parameters with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades. [ABSTRACT FROM AUTHOR]

Let F q be a finite field with q = p e elements, where p is a prime and e is a positive integer. In 2017, Fan and Zhang introduced ℓ -Galois inner products on the n-dimensional vector space F q n for 0 ≤ ℓ < e , which generalized the Euclidean inner product and Hermitian inner product. ℓ -Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes and Hermitian self-orthogonal codes, and can be used to construct entanglement-assisted quantum error-correcting codes. In this paper, we study ℓ -Galois self-orthogonal constacyclic codes of length n over the finite field F q . Sufficient and necessary conditions for constacyclic codes of length n over F q being ℓ -Galois self-orthogonal and ℓ -Galois self-dual are characterized. A sufficient and necessary condition for the existence of nonzero ℓ -Galois self-orthogonal constacyclic codes of length n over F q is obtained. Formulae to enumerate the number of ℓ -Galois self-orthogonal and ℓ -Galois self-dual constacyclic codes of length n over F q are found. In particular, formulae to enumerate the number of Hermitian self-orthogonal and Hermitian self-dual constacyclic codes of length n over F q are obtained. Weight distributions of two classes of ℓ -Galois self-orthogonal constacyclic codes are calculated. A family of MDS ℓ -Galois self-orthogonal constacyclic codes over F q is constructed. [ABSTRACT FROM AUTHOR]

In this paper, we first generalize the polycyclic codes over finite fields to polycyclic codes over the mixed alphabet Z 2 Z 4 , and we show that these codes can be identified as Z 4 [ x ] -submodules of R α , β with R α , β = Z 2 [ x ] / ⟨ t 1 (x) ⟩ × Z 4 [ x ] / ⟨ t 2 (x) ⟩ , where t 1 (x) and t 2 (x) are monic polynomials over Z 2 and Z 4 , respectively. Then we provide the generator polynomials and minimal generating sets for this family of codes based on the strong Gröbner basis. In particular, under the proper defined inner product, we study the dual of Z 2 Z 4 -additive polycyclic codes. Finally, we focus on the characterization of the Z 2 Z 4 -MDSS and MDSR codes, and as examples, we also present some (almost) optimal binary codes derived from the Z 2 Z 4 -additive polycyclic codes. [ABSTRACT FROM AUTHOR]

A Z 2 s -additive code C of length n is a subgroup of Z 2 s n . Carlet (IEEE Trans Inf Theory 44:1543–1547, 1998) introduced a Gray map Φ (Carlet's Gray map) on Z 2 s and Tapia-Recillas and Vega (SIAM J Discret Math 17:103–113, 2003) have been shown that Φ (C) is a binary linear code if and only if for every u , v ∈ C , 2 (u ⊙ v) ∈ C , which their number is ∣ C ∣ 2 - ∣ C ∣ 2 . Let C be a linear code over Z 8 of type { δ 0 , δ 1 , δ 2 } . In this paper, by using the rows of the generator matrix (in standard form) of C , we introduce a set S with ∣ S ∣ ≤ δ 0 (δ 0 + 3) 2 + δ 1 and show that Φ (C) is linear if and only if for every u , v ∈ S , 2 (u ⊙ v) ∈ C . The results show that for a linear code C over Z 8 calculations to check the linearity of Φ (C) are less than Tapia-Recillas and Vega's method. In addition, for a cyclic code of odd length over Z 8 , a condition on the generator polynomial of this code is given which its Carlet's Gray image is linear. Also, as a result, we show that the Carlet's Gray image of a quadratic residue code over Z 8 is not linear. [ABSTRACT FROM AUTHOR]