A class of double-twisted generalized Reed-Solomon codes

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-03-01 DOI:10.1016/j.ffa.2024.102395

Canze Zhu , Qunying Liao

引用次数: 0

Abstract

In this paper, let q be a prime power, we focus on a class of double-twisted generalized Reed-Solomon code $C$ over $F_{q}$ . We give a sufficient and necessary condition for $C$ to be MDS or AMDS, and prove that $C$ is non-GRS by calculating the Schur square of its dual code. Furthermore, we present a sufficient and necessary condition for $C$ to be self-dual, and then construct several classes of self-dual NMDS or non-GRS MDS codes.

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一类双扭广义里德-所罗门码

本文设 q 为质幂，重点研究 Fq 上的一类双扭曲广义里德-所罗门码 C。我们给出了 C 是 MDS 或 AMDS 的充分必要条件，并通过计算其对偶码的舒尔平方证明 C 是非 GRS。此外，我们还给出了 C 是自双码的充分必要条件，然后构建了几类自双 NMDS 或非GRS MDS 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

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.