On Cyclic and Negacyclic Codes of Length 8ps Over Fpm + uFpm

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2020-07-01 DOI:10.18311/jims/2020/23906

Saroj Rani

引用次数: 3

Abstract

In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8p^s over the chain ring Fp^m + uFp^m in terms of their generator polynomials, where u² = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8p^s over Fp^m + uFp^m. Also, we determine μ and -constacyclic codes of length 8p^s over Fp^m + uFp^m.

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Fpm+uFpm上长度为8ps的循环码和反循环码

在本文中，我们根据生成多项式建立了链环Fpm+uFpm上所有长度为8ps的循环码和负循环码的代数结构，其中u2=0，s是正整数，p是奇素数。我们还发现了每个循环码中码字的数量。除此之外，我们还确定了循环码的对偶，并列出了Fpm+uFpm上长度为8ps的自对偶循环码和负循环码。此外，我们还确定了Fpm+uFpm上长度为8ps的μ和-恒循环码。

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 the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.