一类二元低重线性码及其重量分布  

A Class of Binary Linear Codes with Few Weights and Its Weight Distribution

作　　者：张爱仙[1] 李维娜 ZHANG Aixian;LI Weina(School of Sciences,Xi'an University of Technology,Xi'an,Shaanxi,710048,P.R.China)

机构地区：[1]西安理工大学理学院,西安陕西710048

出　　处：《数学进展》2022年第3期569-576,共8页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11401468);Natural Sciences Basic Research Plan in Shaanxi Province(No.2019JQ-333).

摘　　要：线性码在秘密共享方案、认证码、强正则图以及结合方案等领域有广泛应用,已成为编码理论中重要的研究内容.本文利用布尔函数构造了一类二元线性码,并运用Walsh变换完全确定了这类线性码及其对偶码的重量分布.Linear codes have been an interesting topic in coding theory due to their wide applications in secret sharing,authentication codes,strongly regular graphs and association schemes.In this paper,a class of binary linear codes with few weights from Boolean function is constructed and its weight distribution is determined by using Walsh transform and the dual of the linear code is obtained.

关 键 词：线性码 重量分布 布尔函数 WALSH变换 

分 类 号：O157.4[理学—数学]