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In this paper, we present a construction of quantum error-correcting codes (QECCs) codes and entanglement-assisted quantum error-correcting (EAQECCs) using Euclidean hulls and sums of cyclic codes of length n over a family of ring R s = F q + v 1 F q + v 2 F q + ⋯ + v s F q , where q is an odd prime power and v i 2 = v i , v i v j = v j v i = 0 , for i , j = 1 , 2 , 3 , ⋯ , s and i ≠ j . The study delves into various aspects of this construction. We explore the generator polynomials, the dimension of both Euclidean hulls and the sums of cyclic codes over the ring R s . Further, we determine several new QECCs and EAQECCs. This paper claims that our obtained codes have improved parameters (e.g. higher minimum distance or greater dimension) than the existing quantum codes. Moreover, we present some detailed examples that effectively illustrate our findings. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by 'orbifolding' the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q -series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other. [ABSTRACT FROM AUTHOR]

Secret-sharing is a vital topic of cryptography and has widely used in information protection. One technique to the development of secret-sharing schemes is primarily based on error-correcting codes. In this paper, we determine the minimal codewords of relative four-weight codes and have the utility in the secret sharing schemes. [ABSTRACT FROM AUTHOR]

There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over R = F p m [ u ] / ⟨ u 4 ⟩ of length n = p k . For the determination, we explicitly present third torsional degree for all different types of cyclic codes over R of length n. [ABSTRACT FROM AUTHOR]

Given the growing urge for plastic management and regulation in the world, recent studies have investigated the problem of plastic material identification for correct classification and disposal. Recent works have shown the potential of machine learning techniques for successful microplastics classification using Raman signals. Classification techniques from the machine learning area allow the identification of the type of microplastic from optical signals based on Raman spectroscopy. In this paper, we investigate the impact of high-frequency noise on the performance of related classification tasks. It is well-known that classification based on Raman is highly dependent on peak visibility, but it is also known that signal smoothing is a common step in the pre-processing of the measured signals. This raises a potential trade-off between high-frequency noise and peak preservation that depends on user-defined parameters. The results obtained in this work suggest that a linear discriminant analysis model cannot generalize properly in the presence of noisy signals, whereas an error-correcting output codes model is better suited to account for inherent noise. Moreover, principal components analysis (PCA) can become a must-do step for robust classification models, given its simplicity and natural smoothing capabilities. Our study on the high-frequency noise, the possible trade-off between pre-processing the high-frequency noise and the peak visibility, and the use of PCA as a noise reduction technique in addition to its dimensionality reduction functionality are the fundamental aspects of this work. [ABSTRACT FROM AUTHOR]

Perfect error-correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory. Indeed, the classification of the parameters of e-error correcting perfect codes over q-ary alphabets was a very active topic of research in the late 20th century. Consequently, all parameters of perfect e-error-correcting codes were found if e ≥ 3 , and it was conjectured that no perfect 2-error-correcting codes exist over any q-ary alphabet, where q > 3 . In the 1970s, this was proved for q a prime power, for q = 2 r 3 s and for only seven other values of q. Almost 50 years later, it is surprising to note that there have been no new results in this regard and the classification of 2-error-correcting codes over non-prime power alphabets remains an open problem. In this paper, we use techniques from the resolution of the generalised Ramanujan–Nagell equation and from modern computational number theory to show that perfect 2-error-correcting codes do not exist for 172 new values of q which are not prime powers, substantially increasing the values of q which are now classified. In addition, we prove that, for any fixed value of q, there can be at most finitely many perfect 2-error-correcting codes over an alphabet of size q. [ABSTRACT FROM AUTHOR]

The homogeneous weight (metric) is useful in the construction of codes over a ring of integers Z p l (p prime and l ≥ 1 an integer). It becomes Hamming weight when the ring is taken to be a finite field and becomes Lee weight when the ring is taken to be Z 4 . This paper presents homogeneous weight distribution and total homogeneous weight of burst and repeated burst errors in the code space of n-tuples over Z p l . Necessary and sufficient conditions for existence of an (n, k) linear code over Z p l correcting the error patterns with respect to the homogeneous weight are derived. [ABSTRACT FROM AUTHOR]

In order to improve the multi-class assessment performance of transient stability in power systems, a multi-class assessment model that combines the CLV-GAN algorithm with an improved error-correcting output coding technique is proposed in the paper. To address the issue of the small number of unstable samples in power systems, a sample generation model is constructed by combining a dual-encoder VAE with a GAN network. The model generates effective artificial samples to balance the sample ratio between categories by learning the latent distribution of aperiodic and oscillatory unstable samples from the distribution. The decomposition method based on an improved error-correcting output coding algorithm is applied to convert the multi-class problem into a decision fusion issue for binary models. This method improves the overall performance of the multi-class model, particularly significantly increasing the recognition accuracy of discrimination against oscillatory unstable samples and reducing the safety hazards in the operation of power systems. The simulation validation was conducted on the IEEE 39-bus and IEEE 140-bus systems to confirm the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Let p be an odd prime with p ≠ 5 . In this paper, we first provide the structures of repeated-root cyclic codes of length 10 p s over finite fields F p m . We then give two methods of constructing good quantum error-correcting (QEC) codes from repeated-root cyclic codes of length 10 p s over finite fields F p m . By means of the dimensions of repeated-root cyclic codes of length 10 p s over finite fields F p m , we exhibit an effective manner for constructing new EAQEC codes. We show that the usage of these methods brings us many good QEC and EQAEC codes having these advantages: (1) the parameters of our QEC and EQAEC codes are different from all the previous constructions; (2) for repeated-root cyclic codes, our methods allows for easily calculating the dimensions of QEC and EQAEC codes, and the numbers c of pre-shared maximally entangled states of EAQEC codes. [ABSTRACT FROM AUTHOR]

In 2006, Brun, Devetak and Hsieh developed the theory of entanglement-assisted quantum error-correcting codes (EAQECCs), which generalizes that of quantum stabilizer codes. The study of EAQECCs is currently a hot topic in coding theory and quantum information theory. Let q = p e be a prime power and let ℓ be an integer with 0 ≤ ℓ ≤ e - 1 . The ℓ -Galois hulls of MDS codes are an effective tool for constructing MDS EAQECCs. In this paper, we construct twenty-two families of q-ary MDS codes with ℓ -Galois hulls satisfying 2 (e - ℓ) ∣ e , which are not covered by those available in Cao (Galois hulls of MDS codes and their quantum error correction, 2020. https://arxiv.org/abs/2002.12892v2, IEEE Trans Inf Theory 67(12):7964–7984, 2021) when ℓ ≠ e 2 . From these families of MDS codes with ℓ -Galois hulls, we obtain twenty-two families of q-ary MDS EAQECCs. Compared with the MDS EAQECCs from Cao (Galois hulls of MDS codes and their quantum error correction, 2020. https://arxiv.org/abs/2002.12892v2, IEEE Trans Inf Theory 67(12):7964–7984, 2021), some of the MDS EAQECCs constructed in this paper have much larger dimensions. As an application, we give new families of p-ary entanglement-assisted concatenated quantum codes (EACQCs) by combining an arbitrary p-ary [ [ n ′ , e , d ′ ; c ′ ] ] p EAQECC with the q-ary MDS EAQECCs constructed in this paper. It turns out that the parameters of these EACQCs are very flexible, e.g., the possibility of the lengths of these EACQCs is far greater than the one of the lengths of these MDS EAQECCs. [ABSTRACT FROM AUTHOR]

By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three classes of entanglement-assisted quantum error-correcting maximum-distance-separable (EAQMDS) codes are constructed through generalized Reed–Solomon codes. Under our constructions, the minimum distances of our EAQMDS codes are much larger than those of the known EAQMDS codes of the same lengths that consume the same number of bits. Furthermore, some of the lengths of the EAQMDS codes are not divisors of q 2 - 1 , which are completely new and unlike all those known lengths existed before. [ABSTRACT FROM AUTHOR]

Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) play significant roles in quantum information theory. In this paper, we construct several new families of MDS QECCs and MDS EAQECCs by utilizing Hermitian self-orthogonal generalized Reed–Solomon codes. These newly obtained MDS QECCs contain some known classes of MDS QECCs as subclasses and some of them have larger minimum distance. In addition, many q-ary MDS QECCs and MDS EAQECCs in our constructions have length exceeding q + 1 and minimum distance surpassing q 2 + 1 . [ABSTRACT FROM AUTHOR]

The dimension of Euclidean hull for a linear code is an important quantity to determine the parameters of an entanglement-assisted quantum error-correcting (EAQEC, for short) code. In this paper, we study the Euclidean hull of a cyclic code over finite non-chain rings Z 4 + v Z 4 , where v 2 = v . We provide a method of constructing EAQEC codes by means of our results. This construction is applied to obtain numerous new EAQEC codes, and some of them have better parameters than current EAQEC codes available. [ABSTRACT FROM AUTHOR]

Material identification is playing an increasingly important role in various sectors such as industry, petrochemical, mining, and in our daily lives. In recent years, material identification has been utilized for security checks, waste sorting, etc. However, current methods for identifying materials require direct contact with the target and specialized equipment that can be costly, bulky, and not easily portable. Past proposals for addressing this limitation relied on non-contact material identification methods, such as Wi-Fi-based and radar-based material identification methods, which can identify materials with high accuracy without physical contact; however, they are not easily integrated into portable devices. This paper introduces a novel non-contact material identification based on acoustic signals. Different from previous work, our design leverages the built-in microphone and speaker of smartphones as the transceiver to identify target materials. The fundamental idea of our design is that acoustic signals, when propagated through different materials, reach the receiver via multiple paths, producing distinct multipath profiles. These profiles can serve as fingerprints for material identification. We captured and extracted them using acoustic signals, calculated channel impulse response (CIR) measurements, and then extracted image features from the time–frequency domain feature graphs, including histogram of oriented gradient (HOG) and gray-level co-occurrence matrix (GLCM) image features. Furthermore, we adopted the error-correcting output code (ECOC) learning method combined with the majority voting method to identify target materials. We built a prototype for this paper using three mobile phones based on the Android platform. The results from three different solid and liquid materials in varied multipath environments reveal that our design can achieve average identification accuracies of 90% and 97%. [ABSTRACT FROM AUTHOR]

Monte Carlo simulation is performed with uniformly distributed U(0,1) pseudo-random numbers. Because the numbers are generated from a mathematical formula, they will contain some serial correlation, even if very small. This serial correlation becomes embedded in the correlation structure of the response variable. The response variable becomes an asynchronous time series. This leads to hidden errors in the response variable. The purpose of this paper is to illustrate how this happens and how it can be corrected. The method is demonstrated for the case of a simple queue for which the time in the system is known exactly from theory. The paper derives the correlation between an exponential random variable and its antithetic counterpart obtained by power transform with an infinitesimal negative exponent. [ABSTRACT FROM AUTHOR]

In this paper, fault-tolerant and error-correcting 4-bit S-boxes for cryptography applications with multiple error detection and correction are presented. Here, we consider three applicable 4-bit S-boxes, which are used in lightweight block ciphers PRESENT and PRINCE and lightweight hash function SPONGENT as basic circuits for the error-correcting method. The proposed design does not require two-rail checkers for detecting the error and the redundant S-box for repairing the S-box. This reduces the overall area consumption of the proposed design. In the proposed approach, the error-correcting part of the circuit is implemented concurrently with the main circuit of the S-box. Therefore, the four output bits of the S-box are tested individually to improve the efficiency of fault diagnosis. The proposed fault-tolerant S-box method can detect and repair transient and permanent faults simultaneously. In other words, the structure can detect and repair single, double, triple, and quadruple faults at a time. The comparison with the famous fault-tolerant and error-correcting methods shows that the ability of the proposed method to create error-correcting 4-bit S-boxes is acceptable. The performance of S-boxes with error and with our error-correcting method has been investigated in the image encryption. The analyzes show that the proposed method has the desirable results. Also, the area and timing results, in 180 nm CMOS technology, show the proposed structures are comparable in terms of area and delay overheads than those of the other methods. [ABSTRACT FROM AUTHOR]

Privacy-Preserving Fuzzy Commitment Schemes (PPFCS) have emerged as a promising solution for secure Internet of Things (IoT) device authentication, addressing the critical need for privacy and security in the rapidly growing IoT ecosystem. This paper presents a novel PPFCS-based authentication mechanism that protects sensitive user data and ensures secure communication between IoT devices. The proposed scheme leverages error-correcting codes (ECC) and cryptographic hash functions to achieve reliable and efficient authentication. The PPFCS framework allows IoT devices to authenticate themselves without revealing their true identity, preventing unauthorized access and preserving users’ privacy. Furthermore, our PPFCS-based authentication mechanism is resilient against various attacks, such as replay, man-in-the-middle, and brute-force attacks, by incorporating secure random nonce generation and timely key updates. We provide extensive experimental results and comparative analysis, demonstrating that the proposed PPFCS significantly outperforms existing authentication schemes in terms of security, privacy, and computational efficiency. As a result, the PPFCS offers a viable and effective solution for ensuring secure and privacy-preserving IoT device authentication, mitigating the risks associated with unauthorized access and potential data breaches in the IoT ecosystem. [ABSTRACT FROM AUTHOR]

Ensemble learning, online learning and deep learning are very effective and versatile in a wide spectrum of problem domains, such as feature extraction, multi-class classification and retrieval. In this paper, combining the ideas of ensemble learning, online learning and deep learning, we propose a novel deep learning method called deep error-correcting output codes (DeepECOCs). DeepECOCs are composed of multiple layers of the ECOC module, which combines several incremental support vector machines (incremental SVMs) as base classifiers. In this novel deep architecture, each ECOC module can be considered as two successive layers of the network, while the incremental SVMs can be viewed as weighted links between two successive layers. In the pre-training procedure, supervisory information, i.e., class labels, can be used during the network initialization. The incremental SVMs lead this procedure to be very efficient, especially for large-scale applications. We have conducted extensive experiments to compare DeepECOCs with traditional ECOC, feature learning and deep learning algorithms. The results demonstrate that DeepECOCs perform, not only better than existing ECOC and feature learning algorithms, but also related to deep learning ones in most cases. [ABSTRACT FROM AUTHOR]

Error-correcting codes are known to define chiral 2d lattice CFTs where all the U(1) symmetries are enhanced to SU(2). In this paper, we extend this construction to a broader class of length-n codes which define full (non-chiral) CFTs with SU(2)n symmetry, where n = c + c ¯ . We show that codes give a natural discrete ensemble of 2d theories in which one can compute averaged observables. The partition functions obtained from averaging over all codes weighted equally is found to be given by the sum over modular images of the vacuum character of the full extended symmetry group, and in this case the number of modular images is finite. This averaged partition function has a large gap, scaling linearly with n, in primaries of the full SU(2)n symmetry group. Using the sum over modular images, we conjecture the form of the genus-2 partition function. This exhibits the connected contributions to disconnected boundaries characteristic of wormhole solutions in a bulk dual. [ABSTRACT FROM AUTHOR]

The user datagram protocol is the most widely used protocol for streaming multimedia data over the Internet. Like other protocols at the network and transport layers, it uses the Internet Checksum (IC) to detect channel errors. The consequence of this is that each corrupted packet is dropped, which can degrade the quality of service perceived by a user. In this paper, the authors present a solution to this problem based on integer codes capable of correcting single and double adjacent errors. The presented codes are a generalization of the IC, which makes them easy to implement in software. [ABSTRACT FROM AUTHOR]

Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for b-symbol read channels where b ≥ 2 in 2016. In this paper, we establish a b-sphere-packing bound and present a recurrence relationship for the b-weight enumerator. We determine all parameters of linear perfect b-symbol e-error-correcting codes over F q for e < 2 b and show that for 2 b ≤ e < 3 b , there exist at most finite such codes for a given b ,   e , and q. We construct a family of linear perfect b-symbol b-error-correcting codes over F q using constacyclic codes. [ABSTRACT FROM AUTHOR]

The number-theoretic code is a class of codes defined by single or multiple congruences. These codes are mainly used for correcting insertion and deletion errors, and for correcting asymmetric errors. This paper presents a formula for a generalization of the complete weight enumerator for the number-theoretic codes. This formula allows us to derive the weight enumerators and cardinalities for the number-theoretic codes. As a special case, this paper provides the Hamming weight enumerators and cardinalities of the non-binary Tenengolts’ codes, correcting single insertion or deletion. Moreover, we show that the formula deduces the MacWilliams identity for the linear codes over the ring of integers modulo $r$. [ABSTRACT FROM AUTHOR]

In this paper, we present generalized edge-pairings for the family of hyperbolic tessellations {4λ, 4} with the purpose of obtaining the corresponding discrete group of isometries. These tessellations have greater density packing than the self-dual tessellations {4λ, 4λ}, implying that the associated codes achieve the least error probability or, equivalently, that these codes are optimum codes. We also consider the topological quantum error-correcting codes on surfaces with genus g ≥ 2, as proposed in other papers. From that, we focus on the class of topological quantum maximum distance separable codes, showing that the only such codes are precisely the ones with minimum distance d ≤ 2. [ABSTRACT FROM AUTHOR]

The blind quantum computation (BQC) protocol allows for privacy-preserving remote quantum computations. In this paper, we introduce a remote quantum error correction code preparation protocol for BQC using a cluster state and analyze its blindness in the measurement-based quantum computation model. Our protocol requires fewer quantum resources than previous methods, as it only needs weak coherent pulses, eliminating the need for quantum memory and limited quantum computing. The results of our theoretical analysis and simulations show that our protocol requires fewer quantum resources compared to non-coding methods with the same qubit error rate. [ABSTRACT FROM AUTHOR]

The need for fast communication has led to the introduction of 100 Gbps optics in local area networks (LANs). To avoid retransmission of corrupted packets, in some LANs, the CRC codes were replaced by Reed‐Solomon (RS) codes. Although this solution has met its primary goal, it has two drawbacks: first, the payload size was significantly reduced, and second, each network node had to be equipped with much more complex hardware, which increased the cost of the network. Starting from the fact that the vast majority of corrupted packets contain only single errors, in this paper, a simple strategy for error control in 100 Gbps optical LANs is presented. More precisely, instead of protecting the data with the CRC or RS codes, using integer codes is suggested that can correct single errors and detect two types of burst errors: l‐bit burst errors within one b‐bit byte and h‐bit burst errors within two b‐bit bytes (1 ≤ h < l < b). Unlike the CRC or RS codes, the proposed ones use integer and lookup table operations, which are supported by all processors. In addition, the proposed codes can be interleaved without delay and without using any additional hardware. This feature allows the decoder not only to process larger data sets in parallel, but also to detect all double burst errors. [ABSTRACT FROM AUTHOR]

A field dynamic balancer is crucial to the applications of magnetically suspended turbomolecular pumps. Therefore, this paper presents a novel field dynamic balancing method based on autocentering control mode without any additional instrumentation. Firstly, the dynamics of the active magnetic bearing rotor system with unbalance are modeled. Through model analysis, it was found that making the rotor rotate around the geometric axis can improve the accuracy of dynamic balancing. Secondly, the relationship between the correcting masses and the synchronous currents based on the influence coefficient method is established. Then, an autocentering controller is designed to make the rotor rotate around the geometric axis. The synchronous currents can be detected and extracted by the current transducers to calculate the unbalance correction mass. Finally, the experimental results show that this novel field dynamic balancing method can effectively eliminate the majority of rotor unbalance. Compared with the original unbalance of a rotor, the synchronous current in the A-end has been reduced by 71.4% and the synchronous current in the B-end, by 90.8% with the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes an adaptation of a polar code decoding technique in favor of the extended Golay code. Based on the bridge provided by a permutation matrix between the code words of these two classes of codes, the Golay code can be decoded by any polar code technique. Contrary to the successive-cancellation list technique which is characterized by a serial estimation of the bits, we propose in this work an adaptation of the simplified successive-cancellation list technique to polar codes equivalent to the Golay code. The simulations have achieved the performance of a maximum likelihood decoding, with the low decoding complexity of polar codes, compared to one of the universal decoders of linear codes most known in the literature. [ABSTRACT FROM AUTHOR]

Operator quantum error-correcting codes (OQECCs), also known as subsystem codes, can effectively protect quantum information from interference by encoding quantum information in the tensor factor of the subspace of the physical state space. Let R = F q 2 + v F q 2 with v 2 = v and q be an odd prime power. In this paper, by designing some flexible defining sets of the Gray images of Hermitian dual-containing constacyclic codes of length n = q 2 - 1 2 s over R, where s = h ℓ is a divisor of q + 1 , h ≥ 3 is an odd prime and ℓ is a positive integer, we construct two new infinite families of maximum distance separable (MDS) OQECCs with parameters: q 2 - 1 s , q 2 - 1 s - 2 d + 2 - r , r , d q , where 3 ≤ d ≤ q - 1 2 and 0 ≤ r < q 2 - 1 s - 2 d + 2 for ℓ even; q 2 - 1 s , q 2 - 1 s - 2 d + 2 - r , r , d q , where 3 ≤ d ≤ (q + 1) (s + 1) 2 s - 1 and 0 ≤ r < q 2 - 1 s - 2 d + 2 for ℓ odd. Notably, the parameters of these MDS OQECCs are new and not covered by well-known MDS OQECCs constructed from previous literature. [ABSTRACT FROM AUTHOR]

Entanglement-assisted quantum error-correcting codes (EAQECCs) can be constructed from any classical linear codes by using pre-existing entanglement between the sender and receiver. In this paper, we construct a new family of maximum distance separable (MDS) EAQECCs with flexible parameters via constacyclic codes over the finite non-chain ring F q 2 + u F q 2 + ⋯ + u r - 1 F q 2 , where q is a prime power and u r = 1 . Notably, our codes obtained are not covered by the codes available in the previous literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the CSS and Steane's constructions to establish quantum error-correcting codes (briefly, QEC codes) from cyclic codes of length 3 p s over F p m . We obtain several new classes of QEC codes in the sense that their parameters are different from all the previous constructions. Among them, we identify all quantum MDS (briefly, qMDS) codes, i.e., optimal quantum codes with respect to the quantum Singleton bound. In addition, we construct quantum synchronizable codes (briefly, QSCs) from cyclic codes of length 3 p s over F p m . Furthermore, we give many new QSCs to enrich the variety of available QSCs. A lot of them are QSCs codes with shorter lengths and much larger minimum distances than known non-primitive narrow-sense BCH codes. [ABSTRACT FROM AUTHOR]

This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions without resorting to diffusion approximations. Tractability is achieved by generating new offspring using n-parent rather than 2-parent recombination. While this enforces linkage equilibrium among offspring, it allows analysis of the whole population under linkage disequilibrium. We derive a general and exact relationship between fitness fluctuations and response to selection. Our assumptions allow analytical calculation of the stationary distribution of the model for a variety of non-trivial fitness functions. These results allow us to speak to genetic architecture, i.e., what stationary distributions result from different fitness functions. This paper presents methods for exactly deriving stationary states for finite and infinite populations. This method can be applied to many fitness functions, and we give exact calculations for four of these. These results allow us to investigate metastability, tradeoffs between fitness functions, and even consider error-correcting codes. [ABSTRACT FROM AUTHOR]

Integer codes have been successfully applied to various areas of communication and computer technology. They demonstrate good performance in correcting specific kinds of errors. In many cases, the used integer codes are constructed by computer search. This paper presents an algebraic construction of integer codes over the ring of integers modulo A = 2 n + 1 capable of correcting at least up to two bit errors in a single b-byte. Moreover, the codes can correct some configurations of three or more erroneous bits, but not all possible ones. The construction is based on the use of cyclotomic cosets of 2 modulo A. [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]

In this paper, we present a new perspective of single server private information retrieval (PIR) schemes by using the notion of linear error-correcting codes. Many of the known single server schemes are based on taking linear combinations between database elements and the query elements. Using the theory of linear codes, we develop a generic framework that formalizes all such PIR schemes. This generic framework provides an appropriate setup to analyze the security of such PIR schemes. In fact, we describe some known PIR schemes with respect to this code-based framework, and present the weaknesses of the broken PIR schemes in a unified point of view. [ABSTRACT FROM AUTHOR]

In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions, which goes to infinity. Without feedback, it is known that the rate of optimal asymmetric-error-correcting codes for the error fraction $\tau \ge 1/4$ vanishes as the blocklength grows. In this paper, we give an efficient feedback encoding scheme with $n$ transmissions that achieves a positive rate for any fraction of errors $\tau < 1$ and $n\to \infty $. Additionally, we state an upper bound on the rate of asymptotically long feedback asymmetric error-correcting codes. [ABSTRACT FROM AUTHOR]

In this paper, by using the Hamming distance, we establish a relation between quantum error-correcting codes ((N , K , d + 1)) s and orthogonal arrays with orthogonal partitions. Therefore, this is a generalization of the relation between quantum error-correcting codes ((N , 1 , d + 1)) s and irredundant orthogonal arrays. This relation is used for the construction of pure quantum error-correcting codes. As applications of this method, numerous infinite families of optimal quantum codes can be constructed explicitly such as ((3 , s , 2)) s for all s i ≥ 3 , ((4 , s 2 , 2)) s for all s i ≥ 5 , ((5 , s , 3)) s for all s i ≥ 4 , ((6 , s 2 , 3)) s for all s i ≥ 5 , ((7 , s 3 , 3)) s for all s i ≥ 7 , ((8 , s 2 , 4)) s for all s i ≥ 9 , ((9 , s 3 , 4)) s for all s i ≥ 11 , ((9 , s , 5)) s for all s i ≥ 9 , ((10 , s 2 , 5)) s for all s i ≥ 11 , ((11 , s , 6)) s for all s i ≥ 11 , and ((12 , s 2 , 6)) s for all s i ≥ 13 , where s = s 1 ⋯ s n and s 1 , ... , s n are all prime powers. The advantages of our approach over existing methods lie in the facts that these results are not just existence results, but constructive results, the codes constructed are pure, and each basis state of these codes has far less terms. Moreover, the above method developed can be extended to construction of quantum error-correcting codes over mixed alphabets. [ABSTRACT FROM AUTHOR]

In this paper, we use a method inspired by the valuation theory to classify completely cyclic codes of length 3 p s over p m + u p m + u 2 p m . Then, we compute their separation parameters which was useful to compute the Hamming distance in [8]. [ABSTRACT FROM AUTHOR]

This paper studies linear and affine error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to having an information rate at most 1/2 (achieved by the trivial two fold repetition code). Previously, it was (erroneously) reported that more generally no nontrivial linear codes correcting k deletions exist, i.e., that the (k + 1)-fold repetition codes and its rate of 1/(k + 1) are basically optimal for any k. We disprove this and show the existence of binary linear codes of length n and rate just below 1/2 capable of correcting \Omega(n) insertions and deletions. This identifies rate 1/2 as a sharp threshold for recovery from deletions for linear codes and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate vs. (edit) distance trade-off of linear insdel codes. We complement our existential results with an efficient synchronization-string-based transformation that converts any asymptotically good linear code for Hamming errors into an asymptotically good linear code for insdel errors. Last, we show that the 2 -rate limitation does not hold for affine codes by giving an explicit affine code of rate 1 - e epsilon which can efficiently correct a constant fraction of insdel errors. [ABSTRACT FROM AUTHOR]

Data pre-processing is the first step of using SCADA data to study the performance of wind turbines. However, there is a lack of knowledge of how to obtain more effective data pre-processing algorithms. This paper fully explores multiple data pre-processing algorithms for power curve modeling. A three-stage data processing mode is proposed, namely, preliminary data filtering and compensation (Stage I), secondary data filtering (Stage II), and single-valued processing (Stage Ⅲ). Different data processing algorithms are selected at different stages and are finally merged into nine data processing algorithms. A novel evaluation method based on energy characteristic consistency (ECC) is proposed to evaluate the reliability of various algorithms. The influence of sliding mode and benchmark of Binning on data processing has been fully investigated through indicators. Four wind turbines are selected to verify the advantages and disadvantages of the nine data processing methods. The result shows that at the same wind speed, the rotational speed and power values obtained by MLE (maximum likelihood estimation) are relatively high among the three single-valued methods. Among the three outlier filtering methods, the power value obtained by KDE (kernel density estimation) is relatively large. In general, KDE-LSM (least square method) has good performance in general. The sum of four evaluating index values obtained by KDE-LSM from four wind turbines is the smallest. [ABSTRACT FROM AUTHOR]

Certain classical codes can be viewed isomorphically as ideals of group algebras, while studying their algebraic structures help extracting the code properties. Research has shown that this was remarkably efficient in the case when the code generators are idempotents. In quantum error correction, the theory of stabilizer formalism requires classical self-orthogonal additive codes over the finite field GF(4), which, via the lens of group algebras, are essentially F 2 -submodules over GF(4). Therefore, this paper provides a classification on idempotents in commutative group algebra GF(4)G, followed by a criterion that allows idempotents to generate stabilizer subgroups. Later, the construction of quantum stabilizer codes is done in the case when G is a cyclic group C n , for n = 2 m - 1 and n = 2 m + 1 . Quantum bounds on their burst error minimum distance are subsequently determined. [ABSTRACT FROM AUTHOR]

The hull of a linear code is the intersection of itself with its dual code with respect to certain inner product. Both Euclidean and Hermitian hulls are of theorical and practical significance. In this paper, we construct several new classes of maximum distance separable (MDS) codes via (extended) generalized Reed-Solomon (GRS) codes and determine their Euclidean or Hermitian hulls. As a consequence, four new classes of MDS codes with Hermitian hulls of flexible dimensions and six new classes of MDS codes with Euclidean hulls of flexible dimensions are constructed. As applications, for the former, we further construct four new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and four new families of MDS EAQECCs of length n > q + 1 . Meanwhile, many of the distance parameters of our MDS EAQECCs are greater than ⌈ q 2 ⌉ or q; for the latter, we show some examples on Euclidean self-orthogonal and one-dimensional Euclidean hull MDS codes. In addition, two new general methods for constructing extended GRS codes with (k - 1) -dimensional Hermitian hull and Hermitian self-orthogonal extended GRS codes are also provided. [ABSTRACT FROM AUTHOR]

Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty higher dimensional entanglement is not easy. This calls for exploring realistic solutions which are implementable with current devices. Motivated particularly by the difficulty in generation of multiparty entangled states, in this paper, we have investigated error-free information transfer with minimal requirements. For this, we have proposed a new information encoding scheme for communication purposes. The encoding scheme is based on the fact that most noisy channels leave some quantities invariant. Armed with this fact, we encode information in these invariants. These invariants are functions of expectation values of operators. This information passes through the noisy channel unchanged. Pertinently, this approach is not in conflict with other existing error correction schemes. In fact, we have shown how standard quantum error-correcting codes emerge if suitable restrictions are imposed on the choices of logical basis states. As applications, for illustration, we propose a quantum key distribution protocol and an error-immune information transfer protocol. [ABSTRACT FROM AUTHOR]

Passwords are ubiquitous in today's world, as are forgetting and stealing them. Biometric signs are harder to steal and impossible to forget. This paper presents a complete system of methods that takes a secret key and the iris image of the owner as input and generates a public key, suitable for storing insecurely. It is impossible to obtain source data (i.e., secret key or biometric traits) from the public key without the iris image of the owner, the irises of other persons will not help. At the same time, when the iris image of the same person is presented the secret key is restored. The system has been tested on several iris image databases from public sources. It allows storing 65 bits of the secret key, with zero possibility to unlock it with the impostor's iris and 10.4 % probability to reject the owner in one attempt. [ABSTRACT FROM AUTHOR]

Since their rediscovery in the early 1990s, low-density parity-check (LDPC) codes have become the most popular error-correcting codes owing to their excellent performance. An LDPC code is a linear block code that has a sparse parity-check matrix. Cycles in this matrix, particularly short cycles, degrade the performance of such a code. Hence, several methods for counting short cycles in LDPC codes have been proposed, such as Fan's method to detect 4-cycles, 6-cycles, 8-cycles, and 10-cycles. Unfortunately, this method fails to count all 6-cycles, i.e., ignores numerous 6-cycles, in some given parity-check matrices. In this paper, an improvement of this algorithm is presented that detects all 6-cycles in LDPC codes, as well as in general bipartite graphs. Simulations confirm that the improved method offers the exact number of 6-cycles, and it succeeds in detecting those ignored by Fan's method. [ABSTRACT FROM AUTHOR]

This paper proposes an exact algorithm to solve the one-to-one multiobjective shortest path problem. The solution involves determining a set of nondominated paths between two given nodes in a graph that minimizes several objective functions. This study is motivated by the application of this solution method to determine cycling itineraries. The proposed algorithm improves upon a label-correcting algorithm to rapidly solve the problem on large graphs (i.e., up to millions of nodes and edges). To verify the performance of the proposed algorithm, we use computational experiments to compare it with the best-known methods in the literature. The numerical results confirm the efficiency of the proposed algorithm. Summary of Contribution: The paper deals with a classic operations research problem (the one-to-one multiobjective shortest path problem) and is motivated by a real application for cycling itineraries. An efficient method is proposed and is based on a label-correcting algorithm into which several additional improvement techniques are integrated. Computational experiments compare this algorithm with the best-known methods in the literature to validate the performance on large-size graphs (Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) instances from the ninth DIMACS challenge). New instances from the context of cycling itineraries are also proposed. [ABSTRACT FROM AUTHOR]

This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n \times n$ array can experience deletions of rows and columns. These deletion errors are referred to as $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletions if ${t_{\mathrm {r}}}$ rows and ${t_{\mathrm {c}}}$ columns are deleted, while a code correcting these deletion patterns is called a $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletion correction code. The definitions for criss-cross insertions are similar. It is first shown that when $t_{r}=t_{c}$ the problems of correcting criss-cross deletions and criss-cross insertions are equivalent. The focus of this paper lies on the case of (1, 1)-criss-cross deletions. A non-asymptotic upper bound on the cardinality of (1, 1)-criss-cross deletion correction codes is shown which assures that the redundancy is at least $2n-3+2\log n$ bits. A code construction with an existential encoding and an explicit decoding algorithm is presented. The redundancy of the construction is at most $2n+4 \log n + 7 +2 \log e$. A construction with explicit encoder and decoder is presented. The explicit encoder adds an extra $5\log n + 5$ bits of redundancy to the construction. [ABSTRACT FROM AUTHOR]

The paper presents a novel efficient encoding and decoding method for self‐correction and anti‐interference used in big data product tracing system based on the cyclic code theory. The principle of constructing code set is first illustrated. Then the specific encoding and decoding methods suitable for the algebra rules are invented in sequence for efficiency. At last, to test the new coding system, the paper accelerates the decoding time by OpenMP more than 36 times. The error‐correcting code presents its perfect recovery property with a recovery rate of more than 95% under 60% damage rate. In analyzing its efficiency, the encoding process only costs 0.0045 second in average while the time of decoding method will increase with the damage rate's ascending, but it can be controlled within 16 seconds. In comparison to other coding patterns in the references, the newly error‐correcting and anti‐interference coding method achieves a balance in complexity, encoding rate, and decoding time with its priority in recovering rate under the damage rate of 60%. [ABSTRACT FROM AUTHOR]

Optical encoders are widely used in accurate displacement measurement and motion-control technologies. Based on different measurement methods, optical encoders can be divided into absolute and incremental optical encoders. Absolute linear encoders are commonly used in advanced computer numerical control (CNC) machines. The subdivision error within one signal period (SDE) of the absolute linear encoder is vital to the positioning accuracy and low velocity control of CNC machines. In our paper, we study the working principle of the absolute linear encoder. We proposed two methods for reducing the SDE of the absolute linear encoder, a single-field scanning method based on the shutter-shaped Moiré fringe, as well as a method for suppressing harmonics through a phase shift of index grating. We established a SDE measuring device to determine the absolute linear encoder's SDE, which we measured using a constant-speed approach. With our proposed methods, the SDE was reduced from ±0.218 μm to ±0.135 μm, which is a decrease of 38.07%. Our fast Fourier transformation (FFT) analysis of the collected Moiré fringe signals demonstrated that the third-, fifth-, and seventh-order harmonics were effectively suppressed. [ABSTRACT FROM AUTHOR]