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Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory. [ABSTRACT FROM AUTHOR]

Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory, and cryptography. In this paper, some new series of large sets of orthogonal arrays are given by direct construction, juxtaposition construction, Hadamard construction, finite field construction, and difference matrix construction. Subsequently, many new infinite classes of orthogonal arrays are obtained by using these large sets of orthogonal arrays and Kronecker product. [ABSTRACT FROM AUTHOR]

Let n , k and t be non-negative integers. The generalized Johnson graph G (n , k , t) is the graph whose vertices are the k -subsets of the set { 1 , 2 , ... , n } , and two vertices are adjacent if and only if they intersect with t elements. Special cases of generalized Johnson graph include the Kneser graph G (n , k , 0) and the Johnson graph G (n , k , k − 1). These graphs play an important role in coding theory, Ramsey theory, combinatorial geometry and hypergraphs theory. In this paper, we discuss the connectivity properties of the Kneser graph G (n , k , 0) and G (n , k , 1) by their symmetric properties. Specifically, with the help of some properties of vertex/edge-transitive graphs we prove that G (n , k , 0) (5 ≤ 2 k + 1 ≤ n) and G (n , k , 1) (4 ≤ 2 k ≤ n) are super restricted edge-connected. Besides, we obtain the exact value of the restricted edge-connectivity and the cyclic edge-connectivity of the Kneser graph G (n , k , 0) (5 ≤ 2 k + 1 ≤ n) and G (n , k , 1) (4 ≤ 2 k ≤ n) , and further show that the Kneser graph G (n , k , 0) (5 ≤ 2 k + 1 ≤ n) is super vertex-connected and super cyclically edge-connected. [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]

Bernal et al. provided a necessary and sufficient condition for a linear code to be realized as an ideal in a finite group algebra and De La Cruz and Willems proved a similar result for ideals in twisted group algebras. In this paper, we extend this characterization to crossed products. Furthermore, we determine conditions for some crossed product codes to be self-dual. [ABSTRACT FROM AUTHOR]

In general, submarines are designed to optimize operation below the water surface because they spend most of their time underwater. On the other hand, the performance in the free surface condition is also important because submarines face a variety of scenarios to complete operational missions, and the free surface condition is unavoidable for port departure and arrival. In the case of a submarine, the numerical accuracy of the potential theory for seakeeping analysis is excellent in submerged conditions, but it is poor in free surface conditions because of nonlinear effects near the free surface area. In this study, STAR-CCM+ was used as a Reynolds-averaged Navier-Stokes (RANS) solver to estimate the seakeeping performance of a Canadian Victoria Class submarine in irregular waves. The results were compared with those of model tests from a published paper. In addition, the potential theory code was also used to assess the seakeeping performance and compare it with computational fluid dynamics (CFD) results. From the calculation results, the motion responses in irregular waves using CFD showed similar trends to the experimental results. In contrast, motion responses from potential code showed significantly larger values than the experimental results. In conclusion, CFD simulations with irregular waves can be a good solution to predict the seakeeping performance of submarines in free surface conditions. [ABSTRACT FROM AUTHOR]

The construction of quantum maximum-distance-separable (MDS) codes has become one of the major goals in quantum coding theory. In this paper, we construct several classes of Hermitian self-orthogonal generalized Reed–Solomon codes. Based on these classical MDS codes, we obtain several new classes of quantum MDS codes with large minimum distance. It turns out that these constructed quantum MDS codes have fewer constraints on the selection of code length, and in some cases, have larger minimum distance than previous literature. Notably, some of the distance parameters of our codes are greater than $ ({q}/{2})+1 $ (q / 2) + 1. [ABSTRACT FROM AUTHOR]

The predictive coding theory is currently widely accepted as the theoretical basis of perception and chronic perceptual disorders are explained as the maladaptive compensation of the brain to a prediction error. Although this gives us a general framework to work with, it is still not clear who may be more susceptible and/or vulnerable to aberrations in this system. In this paper, we study changes in predictive coding through the lens of tinnitus and pain. We take a step back to understand how the predictive coding system develops from infancy, what are the different neural and bio markers that characterise this system in the acute, transition and chronic phases and what may be the factors that pose a risk to the aberration of this system. Through this paper, we aim to identify people who may be at a higher risk of developing chronic perceptual disorders as a reflection of aberrant predictive coding, thereby giving future studies more facets to incorporate in their investigation of early markers of tinnitus, pain and other disorders of predictive coding. We therefore view this paper to encourage the thinking behind the development of preclinical biomarkers to maladaptive predictive coding. [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]

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights. [ABSTRACT FROM AUTHOR]

Boolean functions used in symmetric-key encryption should have high higher-order nonlinearity to resist several known cryptographic attacks, such as algebraic attacks and low-degree approximation attacks. The higher-order nonlinearity also plays an important role in coding theory and theoretical computer science, since it relates to the covering radius of Reed–Muller codes and the Gowers norm, respectively. It is well-known that bent functions have the highest nonlinearity in an even number of variables and thus they possess the best ability to withstand fast correlation attacks and best affine approximation attacks. However, there is currently limited knowledge regarding the higher-order nonlinearity of bent functions because computing the higher-order nonlinearity, or even providing tight lower bounds, is an extremely hard task. In 1974, Dillon proposed two well-known classes of bent functions based on partial spread (in brief, PS), called PS − and PS + , respectively. He also exhibited a subclass of bent functions in PS − , known as partial spread affine plane(PS a p for short). In this paper, we provide a lower bound on the third-order nonlinearity of the simplest PS a p bent functions in n variables, where n ≥ 6 is even, by calculating the nonlinearities of all second-order derivatives of this kind of bent functions. Compared to the two known lower bounds on the third-order nonlinearity given by Carlet and Tang et al. respectively, our lower bound is much better than these two ones. [ABSTRACT FROM AUTHOR]

Determining the maximum number of unit vectors in Rr$\mathbb {R}^r$ with no pairwise inner product exceeding α$\alpha$ is a fundamental problem in geometry and coding theory. In 1955, Rankin resolved this problem for all α⩽0$\alpha \leqslant 0$, and in this paper, we show that the maximum is (2+o(1))r$(2+o(1))r$ for all 0⩽α≪r−2/3$0 \leqslant \alpha \ll r^{-2/3}$, answering a question of Bukh and Cox. Moreover, the exponent −2/3$-2/3$ is best possible. As a consequence, we obtain an upper bound on the size of a q$q$‐ary code with block length r$r$ and distance (1−1/q)r−o(r1/3)$(1-1/q)r - o(r^{1/3})$, which is tight up to the multiplicative factor 2(1−1/q)+o(1)$2(1 - 1/q) + o(1)$ for any prime power q$q$ and infinitely many r$r$. When q=2$q = 2$, this resolves a conjecture of Tietäväinen from 1980 in a strong form and the exponent 1/3$1/3$ is best possible. Finally, using a recently discovered connection to q$q$‐ary codes, we obtain analogous results for set‐coloring Ramsey numbers. [ABSTRACT FROM AUTHOR]

The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely weighted generalized interval entropy (WGIE), and study it in the context of reliability analysis. Several properties, including monotonicity, bounds and uniqueness of WGIE are investigated. Moreover, the proposed measure is estimated using parametric approach and a simulation study is carried out to demonstrate the performance of the estimates for a real data set. The role of WGIE in reliability modeling has been investigated. We also provide an application of the proposed concept in coding theory. [ABSTRACT FROM AUTHOR]

The second largest eigenvalue of a graph is an important algebraic parameter which is related with the expansion, connectivity and randomness properties of a graph. Expanders are highly connected sparse graphs. In coding theory, Expander codes are Error Correcting codes made up of bipartite expander graphs. In this paper, first we prove the interlacing of the eigenvalues of the adjacency matrix of the bipartite graph with the eigenvalues of the bipartite quotient matrices of the corresponding graph matrices. Then we obtain bounds for the second largest and second smallest eigenvalues. Since the graph is bipartite, the results for Laplacian will also hold for Signless Laplacian matrix. We then introduce a new method called vertex-split of a bipartite graph to construct asymptotically good expander codes with expansion factor D/2 < α < D and ϵ < 1/2 and prove a condition for the vertex-split of a bipartite graph to be k-connected with respect to λ2. Further, we prove that the vertex-split of G is a bipartite expander. Finally, we construct an asymptotically good expander code whose factor graph is a graph obtained by the vertex-split of a bipartite graph. [ABSTRACT FROM AUTHOR]

The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings. In this paper, we present and successfully establish a new approach for linear codes of any finite length over local rings that are not necessarily chains. The main focus of this study is to produce generating characters, MacWilliams identities and generator matrices for codes over singleton local Frobenius rings of order 32. To do so, we first start by characterizing all singleton local rings of order 32 up to isomorphism. These rings happen to have strong connections to linear binary codes and Z 4 codes, which play a significant role in coding theory. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show the potential value of using the constructivist grounded theory (CGT) methodology in the Urban and Regional Planning discipline. This is done by reflecting on the application of the CGT fundamentals defined by Kathy Charmaz, applied in a doctoral thesis in Urban and Regional Planning. The substantive area of research in which the thesis took place was the practical training experience of planners in becoming professionally registered. The thesis collected primary data through interviews with 14 planners who have undergone the process of practical training to record, document, and analyse their experiences as a prerequisite and requirement of professional registration. The use of the CGT methodology provides valuable insight into the registration process of planners in South Africa and encourages doctoral candidates to use CGT methodology with the aim of generating new knowledge and theory in the built environment. This paper recommends that CGT methodology should be encouraged, particularly when contributing to fields that are under-researched, limited, or non-existent. [ABSTRACT FROM AUTHOR]

In the paper Patterson – Wiedemann construction revisited by Gangopadhyay et al. (2006), modifying an idempotent function f : G F ( 2 21 ) → G F ( 2 ) , which corresponds to a ( 337 , ( 127 ) ( 49 ) ) -interleaved sequence whose columns are either all 0’s or 1’s, a balanced function h having Δ h < 2 21 + 1 2 is obtained. In this short note, we find that Δ f is computed incorrectly in their paper (leading to Δ h ≮ 2 21 + 1 2 ) and correct their result by disproving the related conjecture for the 21-variable balanced functions. [ABSTRACT FROM AUTHOR]

The rapid advancement of technology has resulted in significant changes in the field of education. In recent years, the Internet of Things (IoT) and Bayesian network technology have emerged as promising tools for enhancing operations research and teaching performance evaluation. IoT devices and sensors can provide real-time data on student performance, while Bayesian network technology can analyze and predict the complex relationships between various variables. This paper proposes a performance evaluation model based on IoT and Bayesian network technology for operations research teaching. Operations research is a broad discipline with a high level of practicality and applicability. It is widely used in business administration, production planning, traffic management, engineering construction, and financial economics. Using experiments, analysis, and quantification, operations research organizes and manages all types of resources in the system, such as human resources, funds, and goods, and formulates the best business plan. Operations research teaching must combine intuitive geometry and immaterial theorems to improve students' understanding. The methods used in the teaching stage are simple: the teaching content could be more exciting and unintended, and it is difficult to grasp the teaching focus, making accurate evaluation of teaching performance difficult. Therefore, in the Bayesian network, the incremental results and the performance evaluation model of operations research achieve an accuracy of 87.3%. By thoroughly examining the fundamentals of Bayesian network technology, one can offer technical assistance in building an operational research teaching performance evaluation model. To combine with real-world teaching scenarios to assess the likelihood of risky events occurring during instruction and make a teaching performance evaluation model grounded in operational research. The B5 teaching effect has the highest risk probability of teaching work (0.89), and teachers with high professional titles have higher average values. [ABSTRACT FROM AUTHOR]

A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of non-scalar multiplications required to evaluate it. This quantity is also described as its tensor rank, which is the smallest number of rank-1 matrices whose span contains its first slice space. In this paper we derive upper bounds on the tensor ranks of certain classes of 3-tensors and give explicit constructions of sets of rank-1 matrices containing their first slice spaces. We also show how these results can be applied in coding theory to derive upper bounds on the tensor rank of some rank-metric codes. In particular, we compute the tensor rank of some families of F q m -linear codes and we show that they are extremal with respect to Kruskal's tensor rank bound. [ABSTRACT FROM AUTHOR]

One of the extremely useful branches in graph theory is the labeling of a graph. Graph labeling plays a vital role in many fields such as database management, astronomy, coding theory, X-ray crystallography, communication network addressing and radar. A labeling of a connected simple graph G V , E is a map that assign each element in G with a positive integer number. An edge irregular total λ - -labeling is a map β : V G ∪ E G → 1 , 2 , 3 , ... , λ - such that W β h ≠ W β z where W β h and W β z are weights for any two distinct edges. In this case, G has total edge irregularity strength (TEIS) if λ - is minimum. In this paper, a new family of graphs called square snake graphs is defined and denoted by C 4 , n . Moreover, we define some related graphs of square snake graphs named double square snake graph D C 4 , n , triple square snake graph T C 4 , n and m -multiple square snake graph M m C 4 , n . Finally, we determine TEIS for square snake graphs, double square snake graph, triple square snake graph and m -multiple square snake graph, which have many applications in coding theory and physics. [ABSTRACT FROM AUTHOR]

Fuzzy graphs as labeled graphs (fuzzy vertex labeling and fuzzy edge labeling) have many applications in real life such as complex networks, coding theory, medical sciences, communication networks, and management sciences. Also, triangular norms as a special class of functions, have many applications in fuzzy set theory, probability and statistics, and other areas. This paper considers the notations of an inverse fuzzy graph and triangular norms to introduce the new type of graphs as valued-inverse Dombi fuzzy graphs. The valued-inverse Dombi fuzzy graphs are a generalization of inverse fuzzy graphs and are dual to Dombi fuzzy graphs. For any given greater than or equal to one real number, we construct a type of Dombi inverse fuzzy graph and investigate some conditions such that the product and union of Dombi inverse fuzzy graphs be a Dombi inverse fuzzy graph. [ABSTRACT FROM AUTHOR]

Binary codes have a special place in coding theory since they are one of the most commonly used in practice. There are classes of codes specific only to the binary case. One such class is self-complementary codes. Self-complementary linear codes are binary codes that, together with any vector, contain its complement as well. This paper is about binary linear self-complementary codes. A natural goal in coding theory is to find a linear code with a given length n and dimension k such that the minimum distance d is maximal. Codes with these properties are called optimal. Another important issue is classifying the optimal codes, i.e., finding exactly one representative of each equivalence class. In some sense, the classification problem is more general than the minimum distance bounds problem. In this work, we summarize the classification results for self-complementary codes with the maximum possible minimum distance and a length of up to 20. For the classification, we developed a new algorithm that is much more efficient compared to existing ones in some cases. [ABSTRACT FROM AUTHOR]

Sunflower in coding theory is a class of important subspace codes and can be used to construct linear codes. In this paper, we study the minimality of linear codes over F q constructed from sunflowers of size s in all cases. For any sunflower, the corresponding linear code is minimal if s ≥ q + 1 , and not minimal if 2 ≤ s ≤ 3 ≤ q . In the case where 3 < s ≤ q , for some sunflowers, the corresponding linear codes are minimal, whereas for some other sunflowers, the corresponding linear codes are not minimal. [ABSTRACT FROM AUTHOR]

In the fields of combinatorics on words and theory of codes, a two-word language { x , y } is a code if and only if x y ≠ y x . But up to now, corresponding characterizations for a three-word language, which forms a code, have not been completely found. Let X = { x , y , z } be a three-word language and | x | , | y | , | z | be their lengths. When | x | = | y | < | z | , a necessary and sufficient condition for X to be a code was obtained in 2018. If | x | < | y | = | z | ≤ 2 | x | , a necessary and sufficient condition for X to be a code is proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we firstly introduce the Gaussian Leonardo polynomial sequences {GLen(X)}⃵n=0 and we obtain Binet's formula, generating function of this sequence. Moreover, we define the matrix GL(X) in the form of 3 x 3. Finally, we study on the coding and decoding applications of the Leonardo number by using the Leonardo matrix. [ABSTRACT FROM AUTHOR]

Audio data compression is used to reduce the transmission bandwidth and storage requirements of audio data. It is the second stage in the audio mastering process with audio equalization being the first stage. Compression algorithms such as BSAC, MP3 and AAC are used as standards in this paper. The challenge faced in audio compression is compressing the signal at low bit rates. The previous algorithms which work well at low bit rates cannot be dominant at higher bit rates and vice-versa. This paper proposes an altered form of vector quantization algorithm which produces a scalable bit stream which has a number of fine layers of audio fidelity. This modified form of the vector quantization algorithm is used to generate a perceptually audio coder which is scalable and uses the quantization and encoding stages which are responsible for the psychoacoustic and arithmetical terminations that are actually detached as practically all the data detached during the prediction phases at the encoder side is supplemented towards the audio signal at decoder stage. Therefore, clearly the quantization phase which is modified to produce a bit stream which is scalable. This modified algorithm works well at both lower and higher bit rates. Subjective evaluations were done by audio professionals using the MUSHRA test and the mean normalized scores at various bit rates was noted and compared with the previous algorithms. [ABSTRACT FROM AUTHOR]

We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptotic density of MRD codes in the rank metric, and the Critical Problem for combinatorial geometries by Crapo and Rota. In the first part of the paper, we use methods from semifield theory to derive two lower bounds for the density function of full-rank, square MRD codes. The first bound is sharp when the matrix size is a prime number and the underlying field is sufficiently large, while the second bound applies to the binary field. We then take a new look at the Critical Problem for combinatorial geometries, approaching it from a qualitative, often asymptotic, viewpoint. We illustrate the connection between this very classical problem and that of computing the asymptotic density of MRD codes. Finally, in the third part of the paper we study the asymptotic density of some special families of codes in the rank metric, including the symmetric, alternating, and Hermitian ones. In particular, we show that the optimal codes in these three contexts are sparse. [ABSTRACT FROM AUTHOR]

Suppose that you wish to sample a random graph G over n vertices and m edges conditioned on the event that G does not contain a "small" t-size graph H (e.g., clique) as a subgraph. Assuming that most such graphs are H-free, the problem can be solved by a simple rejected-sampling algorithm (that tests for t-cliques) with an expected running time of nO(t). Is it possible to solve the problem in a running time that does not grow polynomially with nt? In this paper, we introduce the general problem of sampling a "random looking" graph G with a given edge density that avoids some arbitrary predefined t-size subgraph H. As our main result, we show that the problem is solvable with respect to some specially crafted k-wise independent distribution over graphs. That is, we design a sampling algorithm for k-wise independent graphs that supports efficient testing for subgraph-freeness in time f(t). nc, where f is a function of t and the constant c in the exponent is independent of t. Our solution extends to the case where both G and H are d-uniform hypergraphs. We use these algorithms to obtain the first probabilistic construction of constant-degree polynomially unbalanced expander graphs whose failure probability is negligible in n (i.e., n (1)). In particular, given constants d > c 1, we output a bipartite graph that has n left nodes and nc right nodes with right-degree of d so that any right set of size at most n (1) expands by factor of (d). This result is extended to the setting of unique expansion as well. We observe that such a negligible-error construction can be employed in many useful settings and present applications in coding theory (batch codes and lowdensity parity-check codes), pseudorandomness (low-bias generators and randomness extractors), and cryptography. Notably, we show that our constructions yield a collection of polynomial-stretch locally computable cryptographic pseudorandom generators based on Goldreich's one-wayness assumption resolving a central open problem in the area of parallel-time cryptography (e.g., Applebaum, Ishai, and Kushilevitz [SIAM J. Comput., 36 (2006), pp. 845-888] and Ishai et al. [Proceedings of the 40th Annual ACM Symposium on Theory of Computing, ACM, 2008, pp. 433-442]). [ABSTRACT FROM AUTHOR]

Since its inception in the sociological field more than fifty years, Grounded Theory Methodology (GTM) has been extended to a range of research areas but there still be confusions and misconceptions about its history and methodological principles. This paper attempts to provide a full theoretical overview of the history of GTM and allows limiting misconceptions about the methodology itself. Drawing upon social sciences perspectives, the paper begins by briefly shedding the light on two major related concepts: Grounded Theory (GT) and Grounded Theory Methodology (GTM). It continues by defining what GTM really means and outlines the reasons behind The Discovery of grounded theory and further focuses on the big split that gave birth to three schools of Grounded Theory Methodology: Glaserian, Straussian and Constructivist GTM. [ABSTRACT FROM AUTHOR]

Since its inception in the sociological field more than fifty years, Grounded Theory Methodology (GTM) has been extended to a range of research areas but there still be confusions and misconceptions about its history and methodological principles. This paper attempts to provide a full theoretical overview of the history of GTM and allows limiting misconceptions about the methodology itself. Drawing upon social sciences perspectives, the paper begins by briefly shedding the light on two major related concepts: Grounded Theory (GT) and Grounded Theory Methodology (GTM). It continues by defining what GTM really means and outlines the reasons behind The Discovery of grounded theory and further focuses on the big split that gave birth to three schools of Grounded Theory Methodology: Glaserian, Straussian and Constructivist GTM. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show the potential value of using the constructivist grounded theory (CGT) methodology in the Urban and Regional Planning discipline. This is done by reflecting on the application of the CGT fundamentals defined by Kathy Charmaz, applied in a doctoral thesis in Urban and Regional Planning. The substantive area of research in which the thesis took place was the practical training experience of planners in becoming professionally registered. The thesis collected primary data through interviews with 14 planners who have undergone the process of practical training to record, document, and analyse their experiences as a prerequisite and requirement of professional registration. The use of the CGT methodology provides valuable insight into the registration process of planners in South Africa and encourages doctoral candidates to use CGT methodology with the aim of generating new knowledge and theory in the built environment. This paper recommends that CGT methodology should be encouraged, particularly when contributing to fields that are under-researched, limited, or nonexistent. [ABSTRACT FROM AUTHOR]

Proof testing is used to remove weak ceramic components from a manufactured batch in turn truncating the lower end of the strength‐failure probability distribution. With proof testing, components are subjected to stresses comparable to those observed during service load histories resulting in the remaining ones having assured minimum reliabilities. The degree to which the reliability of the remaining parts is assured depends on the proof test protocol, which includes multiple variables such as stress level, realistic sampling of flaws, complex geometries, multiaxial stresses, transient loading histories, time‐dependent damage due to slow crack growth and/or fatigue, and change in material behavior due to temperature and/or environmental conditions. This paper advances the early work done on proof test theory, which was limited to simple stress states, to include general stress and material states. The theory introduced in this paper takes into account practical conditions often encountered in industrial applications. This advanced proof test theory was coded into the CARES/Life code (Ceramics Analysis and Reliability Evaluation of Structures/Life). Examples are provided to demonstrate the theory. [ABSTRACT FROM AUTHOR]

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has access to the encoder matrix, which in the combinatorial case is sparse and binary. In this paper we consider the problem of designing a decoder to recover a set of sparse codes from their linear measurements alone, that is without access to encoder matrix. To this end we study the matrix factorisation task of recovering both the encoder and sparse coding matrices from the associated linear measurement matrix. The contribution of this paper is a computationally efficient decoding algorithm, Decoder-Expander Based Factorisation, with strong performance guarantees. Under mild assumptions on the sparse coding matrix and by deploying a novel random encoder matrix, we prove that Decoder-Expander Based Factorisation recovers both the encoder and sparse coding matrix at the optimal measurement rate with high probability and from a near optimal number of measurement vectors. In addition, our experiments demonstrate the efficacy and computational efficiency of our algorithm in practice. Beyond compressed sensing, our results may be of interest for researchers working in areas as diverse as linear sketching, coding theory, matrix compression and dictionary learning. [ABSTRACT FROM AUTHOR]

The purpose of this study is to review journal papers on educational big data research published from 2010 to 2018. A total of 143 papers were selected. The papers were characterized based on three dimensions: (a) educational goals; (b) educational problems addressed; and (c) big data analytical techniques used. A qualitative content analysis approach was conducted to develop a coding scheme for analyzing the selected papers. The results identified four types of educational goals, with a clear predominance of quality assurance. The identification of the most mentioned educational problems resulted in four main concerns: the lack of detecting student behavior modeling and waste of resources; inappropriate curricula and teaching strategies; oversights of quality assurance; and privacy and ethical issues. Concerning the most mentioned big data analytical techniques, the coding scheme revealed that the majority of the papers focused on the educational data mining technique followed by the learning analytics technique. The visual analytics technique was mentioned in a few papers. The results also indicated that the educational data mining technique is the most suitable technique to use for quality assurance and to provide potential solutions for the lack of detecting student behavior modeling and the waste of resources in institutions. [ABSTRACT FROM AUTHOR]

The state‐space realization of linear systems is of utmost importance in linear systems theory. After the realization problem for the time‐invariant case was solved, particular attention was paid to the case of linear periodic systems. Recently, such systems have regained importance, for instance, in the context of coding theory where periodic convolutional encoders play an important role. The majority of the contributions within this area only concern the realization of transfer functions (or impulse responses), thus excluding the case of input/output linear systems without coprime representations. By the end of the eighties of the last century, Jan C. Willems suggested an approach (nowadays known as the behavioral approach) that considers a wider class of systems and allows to overcome this drawback. According to this approach, the central object in a system is its behavior which consists of all the signals that satisfy the system laws (also called system trajectories). Consequently, the behavior of a system with an input/output representation that is not coprime contains more trajectories than the set of input/output signals defined by the system transfer function. Our work takes this fact into account. In previous research conducted by the authors, some results on the realization of periodic behavioral systems were obtained, which, despite their importance, are conservative with respect to the dimension of the obtained realizations. In this paper, we revisit the behavioral periodic realization problem and give further insight into this question. This allows to derive new results and set up an algorithm to compute low‐dimensional state‐space realizations. [ABSTRACT FROM AUTHOR]

Aim. The aim of the article is to understand how Chinese parents draw on their learning beliefs and experiences within the Chinese educational context to make decisions about their children's overseas education, as well as analysing how their learning beliefs are similar or different from East Asian or Western learning beliefs. Methods. The study is based on more than 100 in-depth separate interviews with 22 Chinese families conducted over serval years between 2016 and 2019. Based on interpretative phenomenological analysis and discourse analysis, the results are coded according to the theory of values proposed by Clyde Kluckhohn (1951). These learning values are further coded according to whether they are reflective of the American learning model (EALM), Confucian learning model (CLM), and Confucian learning philosophies. Results. The analysis shows that Chinese parents have displayed similar learning beliefs in socialising their children in the family domain, in their disapproval of the Chinese education system, and in their pursuit of a Western overseas education. The Chinese families' pursuit of a Western education for their children are driven by their cultural leaning beliefs, which are rooted in Confucian heritage culture, and which also echo European American heritage cultures. Conclusion. Many researchers tend to emphasise cultural differences in learning, particularly between Confucian heritage and European American heritage cultures. This paper shows the possibilities of cultural learning values shaping educational choices, expands upon the understanding of Confucian heritage culture, and suggests the similarities between the learning cultures of East Asia and the West. [ABSTRACT FROM AUTHOR]

In this paper, we study the codes Ck(n, q) arising from the incidence of points and k-spaces in PG(n, q) over the field Fp, with q = ph, p prime. We classify all codewords of minimum weight of the dual code Ck(n, q)⊥ in case q ∊ {4,8}. This is equivalent to classifying the smallest sets of even type in PG(n, q) for q ∊{4,8}. We also provide shorter proofs for some already known results, namely, of the best known lower bound on the minimum weight of Ck(n, q)\bot for general values of q, and of the classification of all codewords of Cn-1(n, q) of weight up to 2qn-1. [ABSTRACT FROM AUTHOR]

Energy efficiency (EE) is an important indicator in ultra‐reliable and low‐latency communication (URLLC). Power allocation is considered as an effective method to achieve high EE in URLLC. However, since the EE optimization problem is non‐convex, it is difficult to obtain the analytical solution efficiently. Moreover, to ensure reliable and low‐latency communication within a finite blocklength, the Shannon formula becomes impractical for URLLC. Therefore, finite blocklength coding theory is used to meet the requirements of URLLC. In this paper, the EE problem of URLLC is formulated and the power allocation function is parameterized to be optimized through a deep neural network (DNN). The DNN is trained through the primal‐dual iterative algorithm offline in the unsupervised manner, and can be deployed online to achieve real time power allocation results. The numerical results show the effectiveness of 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]

Concurrent signature is considered as a type of fair exchange protocols. This signature allows two entities to exchange their signature in a fair manner. In that case, the two signatures are ambiguous until an extra piece of information, namely the keystone, is revealed. Consequently, the two signatures become binding to their real signers. Concurrent signatures find applications in different real life scenarios such as auction protocol, fair tendering of contracts, electronic transactions, etc. In this paper, we propose a concurrent signature scheme based on coding theory assumptions as a promising alternative to classical cryptography in the era of quantum computers. Our construction fulfils the security requirements of concurrent signature including correctness, unforgeability, ambiguity and fairness. In addition, our construction presents a practical results for signature size and public key length. For instance, we achieve a signature of size equal to 4:2KB and a public key of length 3200KB for 128 - bits security level, we find an average 96% reduction of the signature public key size. Our construction fulfills all the security requierement and achieves optimal results in terms of public key size. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct the linear code, and its dual which corresponding to classification of projective line PG(1,31), we will present Some important results of coding theory, the generator matrix of every linear code in PG(1,31) is found, A parity check matrix is also found . The mathematical programming language GAP was a main computing tool . [ABSTRACT FROM AUTHOR]

Although emergy theory has made progress in the field of eco‐compensation research, there is still a lack of review articles, summarizing the existing knowledge structure in this area of study. Accordingly, the objective of this paper is to provide a reference for researchers by characterizing the current status of emergy theory in the field of eco‐compensation and to establish the internal logic structure among existing studies, based upon a qualitative analysis of textual data. Inspired by the grounded theory, twelve concepts within five categories of emergy theory were extracted by open, axial, and selective coding of relevant literature. Concepts were extracted from the texts and categories were determined according to the inherent logical relationships among those concepts. The "knowledge structure model of emergy theory in the field of eco‐compensation" was constructed and the following five principal categories were identified: "emergy indicators system," the "integration of methods and theories," "research subjects," "calculation of compensation standards," and "research concerns." Moreover, core and supporting genera were also identified from these five axial codes. Finally, the research focuses and hotspots were explored according to the theoretical frameworks as indicated by the core and supporting genera. The findings of this paper provide a reference for researchers to further promote innovation in the application of emergy theory in the field of eco‐compensation. [ABSTRACT FROM AUTHOR]

Linear codes generated by component functions of perfect nonlinear (PN for short) and almost perfect nonlinear (APN for short) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper is to investigate some binary shortened codes of two families of linear codes from APN functions and some $p$ -ary shortened codes associated with PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and $p$ -ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal. The results of this paper show that the shortening technique is very promising for constructing good codes. [ABSTRACT FROM AUTHOR]

As an algorithmic framework, message passing is extremely powerful and has wide applications in the context of different disciplines including communications, coding theory, statistics, signal processing, artificial intelligence and combinatorial optimization. In this paper, we investigate the performance of a message-passing algorithm called min-sum belief propagation (BP) for the vertex-disjoint shortest $k$ -path problem ($k$ -VDSP) on weighted directed graphs, and derive the iterative message-passing update rules. As the main result of this paper, we prove that for a weighted directed graph $G$ of order $n$ , BP algorithm converges to the unique optimal solution of $k$ -VDSP on $G$ within $O(n^{2}w_{max})$ iterations, provided that the weight $w_{e}$ is nonnegative integral for each arc $e\in E(G)$ , where $w_{max}=\max \{w_{e}: e\in E(G)\}$. To the best of our knowledge, this is the first instance where BP algorithm is proved correct for NP-hard problems. Additionally, we establish the extensions of $k$ -VDSP to the case of multiple sources or sinks. [ABSTRACT FROM AUTHOR]

Linear codes with few weights have applications in consumer electronics, communications, data storage systems, secret sharing, authentication codes, and association schemes. As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure computation of data between two parties. The construction of minimal linear codes with new and desirable parameters is an interesting research topic in coding theory and cryptography. Recently, Mesnager et.al. stated that “constructing linear codes with good parameters from non-weakly regular bent functions is an interesting problem.” The goal of this paper is to construct linear codes with two or three weights from non-weakly regular bent functions over finite fields and analyze the minimality of the constructed linear codes. In doing so, we draw inspiration from a paper by Mesnager in which she constructed linear codes with small weights from weakly regular bent functions based on a generic construction method. First, we recall the definitions of the subsets $B_{+}(f)$ and $B_{-}(f)$ associated with a non-weakly regular bent function $f$. Next, we construct two- or three-weight linear $p$ -ary codes on these sets using duals of the non-weakly regular bent functions that are also bent. We note that the constructed linear codes are minimal in almost all cases. Moreover, when $f$ is a non-weakly regular bent function in a certain subclass of Generalized Maiorana-McFarland bent functions, we determine the weight distributions of the corresponding linear codes. As far as we know, the construction of linear codes from non-weakly regular bent functions over finite fields is first studied in the literature by the second author in his dissertation. [ABSTRACT FROM AUTHOR]