Some Results for Double Cyclic Codes over Fq+vFq+v2Fq.

IF 2.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Entropy Pub Date : 2024-09-20 DOI:10.3390/e26090803

Tenghui Deng, Jing Yang

引用次数: 0

Abstract

Let Fq be a finite field with an odd characteristic. In this paper, we present a new result about double cyclic codes over a finite non-chain ring. Specifically, we study the double cyclic code over Fq+vFq+v2Fq with v3=v, which is isomorphic to Fq×Fq×Fq. This study mainly involves generator polynomials and generator matrices. The generating polynomial of the dual code is also obtained. We show the relationship between the generating polynomials of the double cyclic codes and those of their dual codes. Finally, as an application of these results, we construct some optimal codes over F3.

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Fq+vFq+v2Fq 上双循环码的若干结果

设 Fq 是具有奇特征的有限域。在本文中，我们提出了一个关于有限非链环上双循环码的新结果。具体来说，我们研究了 Fq+vFq+v2Fq 上 v3=v 的双循环码，它与 Fq×Fq×Fq 同构。这项研究主要涉及生成多项式和生成矩阵。我们还得到了对偶码的生成多项式。我们展示了双循环码的生成多项式与其对偶码的生成多项式之间的关系。最后，作为这些结果的应用，我们构造了一些 F3 上的最优码。

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

Entropy PHYSICS, MULTIDISCIPLINARY-

CiteScore

4.90

自引率

11.10%

发文量

1580

审稿时长

21.05 days

期刊介绍： Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.