一类基于向量布尔函数构造的极小二无线性码

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一类基于向量布尔函数构造的极小二无线性码
Minimal Binary Linear Codes from a Class of Vectorial Boolean Functions

DOI: 10.12677/AAM.2022.128349, PDF, 下载: 137 浏览: 227
作者: 吴昊：西北师范大学数学与统计学院，甘肃兰州
关键词: 线性码；极小码；向量布尔函数；重量分布；Linear Code； Minimal Code； Vectorial Boolean Function； Weight Distribution

摘要: 线性码在数据储存、通信、密码学和组合数学等方面都有着重要的应用, 其中的极小线性码可以用来构造具有良好访问结构的秘密共享方案. 本文利用向量布尔函数构造了一类新的二无线性码, 并且利用布尔函数的密码学性质研究了线性码的长度, 维数和重量分布. 结论表明, 所构造的线性码最小距离更大且为宽极小码. 此外, 本文将现有的一些结果推广到一般情形.

Abstract: The applications of linear codes in data storage, communication, cryptography and combinatorial mathematics have been of great importance over the years, among which minimal linear codes can be used to construct secret sharing schemes with good ac- cess structure. In this paper, we construct a new class of binary linear codes using vectorial Boolean functions, and study the length, dimension and weight distribution of linear codes using the cryptographic properties of Boolean functions. The results show that the constructed linear codes have larger minimum distance and are wide minimal codes. At the same time, this article extends some existing results to general situations.

文章引用：吴昊. 一类基于向量布尔函数构造的极小二无线性码[J]. 应用数学进展, 2023, 12(8): 3507-3517. https://doi.org/10.12677/AAM.2022.128349

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