Double circulant codes from cubic cyclotomy

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2025-02-24 DOI:10.1016/j.ffa.2025.102593

Minjia Shi , Xinpeng Bian , Patrick Solé

引用次数: 0

Abstract

We introduce a parametrized family of binary double circulant codes, based on cubic cyclotomy. We determine the parameters for which the codes are self-dual and those for which they are LCD (Linear Complementary Dual). As a bonus, they turn out to be formally self-dual in the latter case. The main theoretical tools are the properties of cyclotomic numbers. Examples in modest length show quasi-optimal formally self-dual codes.

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立方环切开术的双循环代码

本文介绍了基于三次环切开术的二元双循环码的参数化族。我们确定了码是自对偶的参数和码是线性互补对偶的参数。作为奖励，在后一种情况下，它们在形式上是自我双重的。主要的理论工具是环切数的性质。中等长度的例子给出了拟最优形式自对偶码。

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.

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