向量双弯曲函数的少权线性码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-05-28 DOI:10.1016/j.ffa.2025.102660

Zhicheng Wang , Qiang Wang , Shudi Yang

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引用次数: 0

摘要

低权重线性码在秘密共享、认证码、强正则图和关联方案中有着广泛的应用。本文给出了向量双弯曲函数和置换多项式的线性码，使得它们的参数和权值分布可以显式确定。特别是，其中一些是三权最优或几乎最优的代码。作为应用，我们将这些码扩展到构造自正交码，并证明了不对称量子码的存在性。

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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Linear codes with few weights from vectorial dual-bent functions

Linear codes with few weights have wide applications in secret sharing, authentication codes, strongly regular graphs and association schemes. In this paper, we present linear codes from vectorial dual-bent functions and permutation polynomials, such that their parameters and weight distributions can be explicitly determined. In particular, some of them are three-weight optimal or almost optimal codes. As applications, we extend these codes to construct self-orthogonal codes and show the existence of asymmetric quantum codes.

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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.