Results 11 to 20 of about 1,011,482 (281)
More Constructions of 3-Weight Linear Codes
Journal of Mathematics, 2021 Linear codes with few weights have become an interesting research topic and important applications of cryptography and coding theory. In this paper, we apply some ternary near-bent and 2-plateaued functions or r-ary functions to construct more 3-weight ...
Lingyong Ma, Guanjun Li, Fengyan Liu
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Fuzzy linear codes based on nested linear codes
Fuzzy Sets and Systems, 2023 In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested self-orthogonal codes.
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The minimum linear locality of linear codes
CoRR, 2021 Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory on the minimum linear locality of linear codes.
Pan Tan +3 more
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A Mathematical Perspective on Post-Quantum Cryptography
Mathematics, 2022 In 2016, the National Institute of Standards and Technology (NIST) announced an open competition with the goal of finding and standardizing suitable algorithms for quantum-resistant cryptography.
Maximilian Richter +3 more
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Linear Codes over Finite Rings
Trends in Computational and Applied Mathematics, 2005 In this paper we present a construction technique of cyclic, BCH, alternat, Goppa and Srivastava codes over a local finite commutative rings with identity.
A.A. de Andrade, R. Palazzo Jr.
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Multi-block Two Repeated Fixed Burst Error Correcting Linear Codes
Ratio Mathematica, 2022 During the digital transmission of information, errors are bound to occur. The errors may be random or burst errors. In this paper, we have obtained necessary and sufficient conditions for the existence of linear codes over that are capable of ...
Ritu Arora +3 more
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Linear codes resulting from finite group actions [PDF]
Transactions on Combinatorics, 2022 In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same
Driss Harzalla
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Maximum Intersection of Linear Codes and Codes Equivalent to Linear
Journal of Applied and Industrial Mathematics, 2019 Summary: We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound \((q-2)M/q\) attainable for \(q\geqslant 3\) for the size of the intersection of two different pseudolinear codes of the same
Avgustinovich, Sergeĭ Vladimirovich +1 more
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Zero-error Slepian-Wolf Coding of Confined Correlated Sources with Deviation Symmetry [PDF]
, 2013 In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes, Generalized Hamming
Cheng, Samuel, Ma, Rick
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On Weight Spectrum of Linear Codes [PDF]
2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY), 2021 We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors from codes with weight $1$ grows to infinity.
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