与弱正则高原平衡函数相关的线性码  

Linear codes associated with weakly regular plateaued balanced functions

作　　者：张同慧 杨淑娣[1] ZHANG Tonghui;YANG Shudi(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong;School of Mathematics and Statistics,Fujian Normal University,350100,Fuzhou,Fujian,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165 [2]福建师范大学数学与统计学院,福建省福州市350100

出　　处：《曲阜师范大学学报（自然科学版）》2024年第2期57-67,F0002,共12页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12071247);曲阜师范大学研究生学位论文科研创新基金(LWCXS20225)。

摘　　要：运用两个弱正则高原平衡函数,设计适当的定义集,构造基于定义集的多种线性码.利用Walsh变换与指数和的性质确定线性码的重量分布.这些线性码都具有较少的非零重量,可应用于秘密共享方案和结合方案等领域.Several families of linear codes are constructed based on the defining sets by choosing appropriate defining sets from two weakly regular plateaued balanced functions.Their weight distributions are explicitly determined by applying the properties of Walsh transform and exponential sums.These linear codes,which have a few non-zero weights,can be used in the fields such as secret sharing schemes and association schemes.

关 键 词：弱正则高原平衡函数 WALSH变换 线性码 

分 类 号：O157.4[理学—数学]