Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-09-29 DOI:10.1016/j.ffa.2025.102732

Sanjit Bhowmick , Kuntal Deka , Alexandre Fotue Tabue , Edgar Martínez-Moro

引用次数: 0

Abstract

This paper investigates the algebraic structure of complementary pairs of additive cyclic codes over a finite commutative chain ring of odd characteristic. We demonstrate that for every additive complementary pair of additive codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive codes over a finite commutative chain ring of odd characteristic to form an additive complementary pair. Finally, we show that, in the case of a complementary pair of additive cyclic codes over a finite chain ring of odd characteristic, one of the codes is permutation equivalent to the trace dual of the other.

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有限链环上加性循环码的迹对偶和加性互补对

研究了奇特征有限交换链环上加性循环码的互补对的代数结构。证明了对于每一对加性码的加性互补对，其组成码都是自由模。此外，我们还给出了奇数特征的有限交换链环上一对加性码形成加性互补对的充分必要条件。最后，我们证明了在奇数特征的有限链环上的加性循环码的互补对中，其中一个码是另一个码的迹对偶的置换等价。

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.