两类具有少重量的二元线性码构造  

Construction of Two Classes of Binary Linear Code with a Few Weights

作　　者：杨志耀 卓泽朋[1] YANG Zhi-Yao;ZHUO Ze-Peng(School of Mathematics and Statistics,Huaibei Normal University,Huaibei 235000,China)

机构地区：[1]淮北师范大学数学与统计学院,淮北235000

出　　处：《密码学报(中英文)》2024年第6期1308-1319,共12页Journal of Cryptologic Research

基　　金：国家自然科学基金(61902140);福建省自然科学基金(2023J01535);淮北师范大学自然科学基金(2023ZK032)。

摘　　要：具有少重量的线性码在秘密共享方案、结合方案和通信系统等密码领域发挥着重要作用.近年来,通过选取合适的定义集构造满足要求的线性码是编码领域中重要的研究方向.修改直和构造并选择合适的初始bent函数和plateaued函数,本文给出了一种具有少谱值的布尔函数的两类构造,并确定构造所得布尔函数的Walsh谱值分布.进一步,选取所得布尔函数的支撑集作为定义集,构造了具有少重量的线性码,并基于Walsh谱值分布给出这些码的重量分布.本文所构造的线性码为三到六重量的、且存在大量极小线性码.Linear codes with a few weights have important applications in secret sharing scheme,as-sociation scheme,communication systems,etc.In recent years,constructing linear codes from Boolean functions and definition sets is an important research direction in coding field.In this study,by mod-ifying the direct sum construction,some Boolean functions with a few Walsh-spectral are obtained by selecting suitable bent and plateaued functions,and the distribution of its Walsh-spectral are de-termined.Furthermore,the support set of the Boolean function is selected as the definition set to construct linear codes with a few weights,and their explicit weight distribution are given using the Walsh-spectral.The results show that these codes are all three to six weights,and there are a lot of minimal linear codes.

关 键 词：线性码 BENT函数 PLATEAUED函数 WALSH谱 重量分布 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]