Construction of a class of at most three-weight linear codes and the applications

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-12-16 DOI:10.1007/s00200-023-00638-y

Wenhui Liu, Xiaoni Du, Xingbin Qiao

引用次数: 0

Abstract

Linear codes are widely studied due to their important applications in authentication codes, association schemes and strongly regular graphs, etc. In this paper, a class of at most three-weight linear codes is constructed by selecting a new defining set, then the parameters and weight distributions of codes are determined by exponential sums. Results show that almost all the linear codes we constructed are minimal and we also describe the access structures of the secret sharing schemes based on their dual. Especially, the new binary code is a two-weight projective code and based on which a strongly regular graph with new parameters is designed.

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构建一类最多三权线性编码及其应用

由于线性码在认证码、关联方案和强规则图等方面的重要应用，线性码被广泛研究。本文通过选择一个新的定义集，构造了一类最多三权的线性编码，然后通过指数和确定了编码的参数和权重分布。结果表明，我们构造的几乎所有线性编码都是最小的，我们还描述了基于其对偶的秘密共享方案的访问结构。特别是，新的二进制代码是一种双权投影代码，并在此基础上设计了一种具有新参数的强规则图。

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

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.