MacWilliams Identities of the Linear Codes Over $${\mathbb {F}}_q\times ({\mathbb {F}}_q+v{\mathbb {F}}_q)$$

IF 1 3区数学 Q1 MATHEMATICS Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-09-02 DOI:10.1007/s40840-024-01760-x

Mevlüt Tekkoyun, Ergün Yaraneri

引用次数: 0

Abstract

Let R be the ${\mathbb {F}}_q$-algebra ${\mathbb {F}}_q\times ({\mathbb {F}}_q+v{\mathbb {F}}_q)$ of order $q^3$ where $v^2=v$ and ${\mathbb {F}}_q$ is a finite field of q elements. We study the MacWilliams identities of the linear codes over R related to complete, Hamming, symmetric, Gray and Lee weight enumerators.

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超过 $${\mathbb {F}}_qtimes ({\mathbb {F}}_q+v{\mathbb {F}}_q)$$ 的线性编码的麦克威廉斯特性

让 R 成为阶为 $q^3$ 的 ${\mathbb {F}}_q$- 代数 ${\mathbb {F}}_q+v\{mathbb {F}}_q)\ 次，其中 \(v^2=v$ 和 ${\mathbb {F}}_q$ 是一个包含 q 个元素的有限域。我们研究了与完全、汉明、对称、格雷和李权重枚举器相关的 R 上线性编码的麦克威廉斯特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.

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