论群码的平方码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-12-10 DOI:10.1016/j.ffa.2024.102548

Alejandro Piñera Nicolás , Ignacio Fernández Rúa , Adriana Suárez Corona

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引用次数: 0

摘要

近年来，纠错码在抗量子密码学中的应用越来越受到人们的关注。它们的适用性取决于它们与随机代码的不可区分性。从这个意义上说，对特定代码的平方码的研究提供了一种区分随机代码和非随机代码的工具。在此动机下，本文研究了一些半简单双边群码的平方码，如阿贝尔群码和二面体群码。为此，利用群的绝对不可约特性，将双边群码描述为评价码。最后，在这种替代观点下，得到了一些关于自对偶性和自正交性的结果。

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On the square code of group codes

Error correcting codes have recently gained more attention due to their applications in quantum resistant cryptography. Their suitability depends on their indistinguishability from random codes. In that sense, the study of the square code of a particular code provides a tool for distinguishing random codes from not random ones.

With this motivation, the square codes of some semisimple bilateral group codes, as abelian and dihedral ones, are studied in this paper. For this purpose, bilateral group codes are described as evaluation codes by means of the absolutely irreducible characters of the group. Finally, some results on self-duality and self-orthogonality are recovered under this alternative point of view.

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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.