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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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