Results 11 to 20 of about 516,863 (164)
Minimal Linear Codes Constructed from Sunflowers
Entropy, 2023 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 Fq constructed from sunflowers of size s in all cases.
Xia Wu, Wei Lu
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Syndrome spectrums of error orbits in RS-codes
Системный анализ и прикладная информатика, 2020 This article is devoted to the research of the properties of syndromes of errors in Reed-Solomon codes. RS-codes are built on non-binary alphabets. So, unlike BCH-codes, RS-codes contain an extremely large variety of correctable errors.
V. A. Lipnitski, S. I. Semyonov
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Linear Codes from Two Weakly Regular Plateaued Balanced Functions
Entropy, 2023 Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes.
Shudi Yang, Tonghui Zhang, Ping Li
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Lee Weight and Generalized Lee Weight for Codes Over $Z_{2^n}$ [PDF]
Mathematics Interdisciplinary Research, 2023 Let $\mathbb{Z}_m$ be the ring of integers modulo $m$ in which $m=2^n$ for arbitrary $n$. In this paper, we will obtain a relationship between $wt_L(x), wt_L(y)$ and $wt_L(x+y)$ for any $x, y \in \mathbb{Z}_m$.
Farzaneh Farhang Baftani
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On the generalized Hamming weights of certain Reed–Muller-type codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a ...
González-Sarabia Manuel +2 more
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A New Code Based Signature Scheme for Blockchain Technology
Mathematics, 2023 Blockchain is a method of recording information that makes it not feasible for the system to be replaced, attacked, or manipulated. A blockchain is equipped with a notebook that copies and processes the various procedures across the network of computers ...
Adel Alahmadi +5 more
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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 automorphisms and error orbits of Reed – Solomon codes
Доклады Белорусского государственного университета информатики и радиоэлектроники, 2020 The purpose of this work with its results presented in the article was to develop and transfer to the class of Reed – Solomon codes (RS-codes) the basic provisions of the theory of syndrome norms (TNS), previously developed for the noise-resistant coding
S. I. Semyonov, V. A. Lipnitsky
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On Some Families of Codes Related to the Even Linear Codes Meeting the Grey–Rankin Bound
Mathematics, 2022 Bounds for the parameters of codes are very important in coding theory. The Grey–Rankin bound refers to the cardinality of a self-complementary binary code. Codes meeting this bound are associated with families of two-weight codes and other combinatorial
Iliya Bouyukliev +2 more
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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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