有限域上长度为 kslmpn 的重复根常环码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-11-14 DOI:10.1016/j.ffa.2024.102542

Qi Zhang , Weiqiong Wang , Shuyu Luo , Yue Li

引用次数: 0

摘要

对于不同的奇数素数 k、l、p 和正整数 s、m、n，Fq[x] 中的多项式 xkslmpn-λ 被显式因式分解，其中 p 是 Fq 的特征，λ∈Fq⁎。表征了 Fq 上长度为 kslmpn 的所有重复根常环码及其对偶码。此外，还得到了 Fq 上所有长度为 kslmpn 的线性互补对偶（LCD）循环码和负循环码的特征和枚举。

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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Repeated-root constacyclic codes of length kslmpn over finite fields

For different odd primes k, l, p, and positive integers s, m, n, the polynomial

x^{k^{s} l^{m} p^{n}} - λ

F_{q} [x]

is explicitly factorized, where p is the characteristic of

F_{q}

λ \in F_{q}^{⁎}

. All repeated-root constacyclic codes and their dual codes of length

k^{s} l^{m} p^{n}

over

F_{q}

are characterized. In addition, the characterization and enumeration of all linear complementary dual (LCD) cyclic and negacyclic codes of length

k^{s} l^{m} p^{n}

over

F_{q}

are obtained.

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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.