Results 41 to 50 of about 563,145 (166)
Group Codes Over Dihedral Group Algebras 𝔽q[D16] and 𝔽q[Z2 × D8]
Journal of MathematicsLet Fq denote a finite field of characteristic p, where q=pk for some prime p and integer k. Let Dn represent a dihedral group of order n. In this paper, group codes in the dihedral group algebras FqD16 and FqZ2×D8 are proposed.
Zhihao Tian, Yanyan Gao
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Complementary dual abelian codes in group algebras of some finite abelian groups [PDF]
ITM Web of ConferencesLinear complementary dual codes have become an interesting sub-family of linear codes over finite fields since they can be practically applied in various fields such as cryptography and quantum error-correction. Recently, properties of complementary dual
Jitman Somphong
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Abelian Group Codes for Channel Coding and Source Coding [PDF]
IEEE Transactions on Information Theory, 2015 In this paper, we study the asymptotic performance of Abelian group codes for the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels as well as the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources.
Aria Ghasemian Sahebi +1 more
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Minimal group codes over alternating groups
, 2023 In this work we show that every minimal code in a semisimple group algebra $\mathbb{F}_qG$ is essential if $G$ is a simple group. Since the alternating group $A_n$ is simple if $n=3$ or $n\geq 5$, we present some examples of minimal codes in $\mathbb{F}_qA_n$.
de Araujo, Robson Ricardo +2 more
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The Dynamics of Group Codes: Dual Abelian Group Codes and Systems [PDF]
IEEE Transactions on Information Theory, 2004 Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces.
Forney Jr., G. David, Trott, Mitchell D.
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Rank-metric codes as ideals for subspace codes and their weight properties
AKCE International Journal of Graphs and Combinatorics, 2019 Let q=pr, p a prime, r a positive integer, and Fqthe Galois field with cardinality q and characteristic p. In this paper, we study some weight properties of rank-metric codes and subspace codes. The rank weight is not egalitarian nor homogeneous, and the
Bryan S. Hernandez, Virgilio P. Sison
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Isometry groups of combinatorial codes [PDF]
Electronic Notes in Discrete Mathematics, 2017 Two isometry groups of combinatorial codes are described: the group of isometries, that is, the group of Hamming isometries from a code to itself and the group of monomial isometries, which is the group of those isometries of a code to itself that extend to monomial maps.
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Higher-group symmetry in finite gauge theory and stabilizer codes
SciPost PhysicsA large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group global symmetry
Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin, Ryohei Kobayashi
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Research on fractional repetition codes based on group divisible designs
Tongxin xuebao, 2015 A novel design of FR (fractional repetition) codes was proposed which aims at providing efficient repair at the minimum bandwidth regenerating point.The design consisted of an outer MDS (maximum distance separable) code and an inner repetition code ...
Bing ZHU +4 more
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The Construction of Permutation Group Codes for Communication Systems: Prime or Prime Power?
IEEE Access, 2020 This paper focuses on correcting a theorem relating to the construction of permutation group codes (PGCs). The theorem in question assumed that affine transformation could be used to enumerate all the code words of a permutation array with a minimum ...
Li Peng, Sijia Chen, Shuxia Guo
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