一类基于布尔函数的极小线性码的构造
Construction of a Class of Minimal Binary Linear Code Based on Boolean Function
DOI: 10.12677/PM.2021.119179, PDF,   
作者: 杜佳玮：西北师范大学数学与统计学院，甘肃 兰州
关键词: 布尔函数；Bent函数；Walsh变换；二元线性码；Boolean Function； Bent Function； Walsh Transform； Binary Linear Code
摘要: 具有较低重量的线性码在数据存储系统、设计具有良好访问结构的秘密共享方案等领域有着重要的应用。基于布尔函数的Walsh谱值分布，该文利用一类具有五值Walsh谱的布尔函数构造了一类具有六重的线性码，确定了码的参数及其重量分布，并编制Magma程序验证了结论的正确性。结果表明，所构造的码为不满足A~B条件的极小线性码，且可用来设计具有良好访问结构的秘密共享方案。
Abstract: Linear codes with few-weight have important applications in data storage system and designing the secret sharing scheme with good access structures. Based on the Walsh spectrum distribution of Boolean function, this paper constructs a class of Boolean functions with five-valued Walsh spectra. The type of six-weight linear code is derived from this new function, and parameters of the code such as length and dimension are determined. And magma program is used to verify the correctness of the conclusion. The results show that the new code is minimal linear code which does not satisfy the A-B condition, and it can be used to design the secret sharing scheme with good access structures.
文章引用：杜佳玮. 一类基于布尔函数的极小线性码的构造[J]. 理论数学, 2021, 11(9): 1623-1629. https://doi.org/10.12677/PM.2021.119179

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