Decoding algorithms in group codes

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-07-07 DOI:10.1016/j.ffa.2025.102692

C. Martínez, F. Molina, A. Piñera-Nicolás

引用次数: 0

Abstract

Group codes are linear codes that can be identified with (two-sided) ideals of a group algebra

K G

. Assuming that

K G

is semisimple, we use its decomposition as the direct sum of two ideals, one of them the group code, to design two decoding algorithms. The first one generalizes Meggitt's algorithm designed for cyclic codes, while the other one is inspired in the decoding algorithm studied in [10] and aims to improve it.

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组码译码算法

群码是可以用群代数KG的（双面）理想识别的线性码。假设KG是半简单的，我们将其分解为两个理想的直接和，其中一个是群码，来设计两种解码算法。第一个是对循环码设计的Meggitt算法的推广，另一个是受到[10]研究的译码算法的启发，旨在对其进行改进。

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.