MDS and MHDR Cyclic Codes over Finite Chain Rings

IF 1.3 4区数学 Q1 MATHEMATICS

Journal of Mathematics Pub Date : 2024-01-25 DOI:10.1155/2024/4540992

Monika Dalal, Sucheta Dutt, Ranjeet Sehmi

引用次数: 0

Abstract

This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code. Furthermore, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code are obtained. Finally, to support our results, some examples of optimal cyclic codes are presented.

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有限链环上的 MDS 和 MHDR 循环码

这项研究为有限链环上的循环码建立了一组唯一的生成器。为此，我们首先确定了码的最小跨集和秩。此外，我们还获得了循环码成为 MDS 码和循环码成为 MHDR 码的充分条件和必要条件。最后，为了支持我们的结果，我们给出了一些最优循环码的例子。

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

Journal of Mathematics Mathematics-General Mathematics

CiteScore

2.50

自引率

14.30%

发文量

期刊介绍： Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.