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三类基于二对一函数构造的二元极小线性码

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极小线性码在秘密共享方案和两方安全计算中具有重要作用。基于具有良好密码学性质的二对一函数,构造了三类线性码;利用函数的Walsh谱值分布,确定了三类线性码的参数及其精确的重量分布。结果表明,构造的三类线性码满足Ashikhmin-Barg条件,均为极小线性码。
Three classes of binary minimal linear codes from 2-to-1 functions
Minimal linear codes have important applications in secret sharing schemes and two-party secure computation.Based on 2-to-1 functions with good cryptographic properties,this paper constructs three classes of linear codes.From the distributions of Walsh spectrum values of the functions,the parameters and accurate weight distributions of the three classes of linear codes are determined.The results show that our linear codes are minimal,which satisfy the Ashikhmin-Barg condition.

binary linear codeminimal code2-to-1 functionAshikhmin-Barg condition

刘芳芳、卓泽朋、陈国龙

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淮北师范大学 数学与统计学院,安徽 淮北 235000

蚌埠学院计算机工程学院,安徽蚌埠 233030

二元线性码 极小码 二对一函数 Ashikhmin-Barg条件

2025

西北师范大学学报(自然科学版)
西北师范大学

西北师范大学学报(自然科学版)

影响因子:0.463
ISSN:1001-988X
年,卷(期):2025.61(1)