几类 p 元线性码的构造

doi:10.12677/PM.2023.135142

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几类 p 元线性码的构造
Construction of Several Classes of p-AryLinear Codes

DOI: 10.12677/PM.2023.135142, PDF, HTML, 下载: 277 浏览: 413
作者: 刘文辉：西北师范大学，数学与统计学院，甘肃兰州
关键词: 线性码；定义集；指数和；重量分布；Linear Code； Defining Set； Exponential Sum； Weight Distribution

摘要: 低重线性码因在秘密共享方案、认证码、结合方案、强正则图等方面具有重要的应用，所以被广泛研究。本文通过选取新的定义集，构造了几类新的 p 元线性码，并利用指数和理论确定了码的参数和重量分布，最后说明本文构造的线性码在多数情况下是极小码，可以用来设计具有良好访问结构的秘密共享方案。

Abstract: Linear codes with a few weights are widely studied due to their important applications in secret sharing schemes, authentication codes, association schemes, strongly regular graphs, etc. In this paper, several classes of p-ary linear codes are constructed by selecting a new definition set, and the parameters and weight distributions of the codes are determined by exponential sums. Finally, it is shown that the linear codes constructed in this paper are minimal linear codes in most cases, which can be used to design secret sharing schemess with good access structures.

文章引用：刘文辉. 几类 p 元线性码的构造[J]. 理论数学, 2023, 13(5): 1389-1402. https://doi.org/10.12677/PM.2023.135142

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