On optimal constant weight codes derived from $$\omega $$ -circulant balanced generalized weighing matrices

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-14 DOI:10.1007/s10623-024-01414-w

Hadi Kharaghani, Thomas Pender, Vladimir Tonchev

引用次数: 0

Abstract

Balanced generalized weight matrices are used to construct optimal constant weight codes that are monomially inequivalent to codes derived from the classical simplex codes. What’s more, these codes can be assumed to be generated entirely by $\omega $-shifts of a single codeword where $\omega $ is a primitive element of a Galois field. Additional constant weight codes are derived by projecting onto subgroups of the alphabet sets. These too are shown to be optimal.

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关于从$$\omega $$ -circulant平衡广义称重矩阵推导出的最优恒权码

平衡广义权重矩阵被用来构造最优恒权码，这些恒权码与由经典单纯形码派生的码在单体上是不等价的。更重要的是，这些编码可以假定完全由单个编码词的（\omega \）移位产生，其中（$\omega $是伽罗瓦域的基元。通过投影到字母集的子群上，还衍生出了其他恒权码。这些编码也被证明是最优的。

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.