来自平面函数的线性编码及相关覆盖编码

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-10-31 DOI:10.1016/j.ffa.2024.102535

Yanan Wu, Yanbin Pan

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引用次数: 0

摘要

权重较小的线性编码在消费类电子产品、数据存储系统和秘密共享中有着广泛的应用。本文利用平面函数，构建了多个 Fp 上 l 权重线性编码的无穷族，其中 l 可以是任意正整数，p 是素数。这些编码的权重分布完全是通过利用指数和的某些方法确定的。实验表明，根据我们的结果可以生成一些（几乎）小维度的最优编码。此外，我们还研究了相关的覆盖码。

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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Linear codes from planar functions and related covering codes

Linear codes with few weights have wide applications in consumer electronics, data storage system and secret sharing. In this paper, by virtue of planar functions, several infinite families of l-weight linear codes over

F_{p}

are constructed, where l can be any positive integer and p is a prime number. The weight distributions of these codes are determined completely by utilizing certain approach on exponential sums. Experiments show that some (almost) optimal codes in small dimensions can be produced from our results. Moreover, the related covering codes are also investigated.

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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.