Results 1 to 10 of about 563,145 (166)
Group codes over symmetric groups
AIMS Mathematics, 2023 Let $ \Bbb F_{q} $ be a finite field of characteristic $ q $ and $ S_n $ a symmetric group of order $ n! $. In this paper, group codes in the symmetric group algebras $ \Bbb F_{q}S_n $ with $ q > 3 $ and $ n = 3, 4 $ are proposed.
Yanyan Gao , Yangjiang Wei
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Group codes over binary tetrahedral group
Journal of Mathematical Cryptology, 2022 In this article, the group algebra K[T]{\mathcal{K}}\left[{\mathscr{T}}] of the binary tetrahedral group T{\mathscr{T}} over a splitting field K{\mathcal{K}} of T{\mathscr{T}} with char(K)≠2,3{\rm{char}}\left({\mathcal{K}})\ne 2,3 is studied and the ...
Dadhwal Madhu, Pankaj
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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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Representing group codes as permutation codes [PDF]
1999 Information Theory and Networking Workshop (Cat. No.99EX371), 1999 Summary: Given an abstract group \({\mathcal G}\), an \(N\)-dimensional orthogonal matrix representation \(G\) of \({\mathcal G}\), and an ``initial vector'' \(x\in \mathbb{R}^N\), Slepian defined the group code generated by the representation \(G\) to be the set of vectors \(Gx\). If \(G\) is a group of permutation matrices, the set \(Gx\) is called a
BIGLIERI E. +2 more
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Optimum commutative group codes [PDF]
Designs, Codes and Cryptography, 2013 A method for finding an optimum $n$-dimensional commutative group code of a given order $M$ is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed.
Torezzan, Cristiano +3 more
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, 2019 International Conference on Algebra, Codes and Cryptology (1st. 2019. Dakar, Senegal) Granted by MTM2017-83506-C2-2-P, FD-GRUPIN-IDI/2018/000193 and RFBR grant 17-01-00895 A.
González Jiménez, Santos +3 more
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Group LCD and group reversible LCD codes
Finite Fields and Their Applications, 2022 In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the $n \times n$ matrices to obtain LCD codes. Our construction method guarantees that our LCD codes are also group codes, namely, the codes are ideals in a group ring.
Steven T. Dougherty +3 more
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Constructions of Orbit Codes Based on Unitary Spaces Over Finite Fields
IEEE Access, 2021 Orbit codes, as special constant dimension codes, have attracted much attention due to their applications for error correction in random network coding. This paper is devoted to constructing large orbit codes by making full use of unitary space. Firstly,
Shangdi Chen, Qin Xu
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Optimizing Regeneration Time by Node Selection in Group Repair Code [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2022 Distributed storage systems use network coding techniques like replication, erasure codes, local codes, regeneration codes, hybrid code, double code and group repair code to store data efficiently and provide speedy recovery of data during failures.
Swati Mittal +3 more
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The Support Splitting Algorithm for Induced Codes
Моделирование и анализ информационных систем, 2018 In the paper, the analysis of the stability of the McEliece-type cryptosystem on induced codes for key attacks is examined. In particular, a model is considered when the automorphism group is trivial for the base code C, on the basis of which the induced
Yury V. Kosolapov, Aleksey N. Shigaev
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