On the duality of cyclic codes of length ps over Fpm[u]〈u3〉

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-09-04 DOI:10.1016/j.ffa.2024.102500

Ahmad Erfanian , Roghaye Mohammadi Hesari

引用次数: 0

Abstract

In this paper, we determine the dual codes of cyclic codes of length $p^{s}$ over $R_{3} = \frac{F_{p^{m}} [u]}{〈 u^{3} 〉}$ , where p is a prime number and $u^{3} = 0$ . Also, we improve and give correction of the results stated by B. Kim and J. Lee (2020) in [11]. Finally, we provide some examples of optimal and near-MDS cyclic codes of length $p^{s}$ over $R_{3}$ and compute dual of them.

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论Fpm[u]〈u3〉上长度为ps的循环码的对偶性

在本文中，我们确定了 R3 上长度为 ps 的循环码的对偶码=Fpm[u]〈u3〉，其中 p 是素数且 u3=0。同时，我们改进并修正了 B. Kim 和 J. Lee (2020) 在 [11] 中所述的结果。最后，我们举例说明了 R3 上长度为 ps 的最优和近 MDS 循环码，并计算了它们的对偶性。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.