一类基于Kasami函数的极小线性码的构造

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一类基于Kasami函数的极小线性码的构造
Construction of a Class of Minimal Linear Codes Based on Kasami Functions

DOI:10.12677/AAM.2023.128361,PDF,下载: 252浏览: 301
作者:张莹中：西北师范大学，数学与统计学院，甘肃兰州
关键词:布尔函数；Walsh变换；极小线性码；Boolean Function；Walsh Transform；Minimal Linear Codes

摘要:布尔函数和线性码在设计序列密码共享方案等方面有重要的应用。本文基于Kasami函数构造了一类具有五值Walsh谱的布尔函数，研究了新函数的Walsh谱值分布，利用新函数构造了一类五重极小线性码。

Abstract:Boolean functions and linear codes with few-weights have important applications in designing sequence ciphers and in designing shared schemes. In this paper, we con- struct a class Boolean functions with five-valued Walsh spectra using Kasami functions and investigate the distribution of Walsh spectral values of the new functions. Final- ly, a class of minimal linear codes with five-weights is constructed by using the new functions.

文章引用：张莹中. 一类基于Kasami函数的极小线性码的构造[J]. 应用数学进展, 2023, 12(8): 3631-3638. https://doi.org/10.12677/AAM.2023.128361

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