Two classes of twisted generalized Reed-Solomon codes with two twists

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-02-18 DOI:10.1016/j.ffa.2025.102595

Shudi Yang , Jinlong Wang , Yansheng Wu

引用次数: 0

Abstract

MDS codes, abbreviated from maximum distance separable codes, hold significant importance in coding theory owing to their good algebraic structures, alongside intriguing practical applications. In this paper, we mainly study two classes of twisted generalized Reed-Solomon codes with two twists. Specifically, some sufficient and necessary conditions for these codes to be MDS or self-orthogonal are obtained; two explicit constructions of MDS self-orthogonal codes are presented; and finally, several classes of linear complementary dual codes via twisted generalized Reed-Solomon codes are also provided.

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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.