一些三重线性码的完备重量计数器  

The Complete Weight Enumerators for Some Three-weight Linear Codes

作　　者：谭婷 朱灿泽 廖群英 Tan Ting;Zhu Canze;Liao Qunying(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]四川师范大学数学科学学院,成都610066

出　　处：《数学理论与应用》2022年第4期19-35,共17页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.12071321)资助。

摘　　要：对于奇素数p,本文通过定义集的方法构造一些p元三重线性码,并利用有限域Fp上的Weil和,确定这些码的完备重量计数器.此外,证明这些码在某些条件下为极小码,进而适用于秘钥共享方案.特别地,得到一类参数为[p^(2)-1,3,p^(2)-p-1]且达到Griesmer界的最优码.本文完善了简高鹏等在文献[1]中得到的部分结果.In this paper,for an odd prime p,some p-element three-weight linear codes are constructed by defining set,and the complete weight enumerators of those codes are determined by using Weil sums over the finite field Fp.Furthermore,it is proved that those codes are minimal under certain conditions,and thus suitable for secret sharing schemes.Especially,a class of those codes with parameters[p^(2)-1,3,p^(2)-p-1]are obtained,which are optimal with respect to the Griesmer bound.Our results can be regarded as improvements to some results of Jian et al.in[1].

关 键 词：三重线性码 完备重量计数器 Weil和 Griesmer界 极小码 密钥共享方案 

分 类 号：O157.4[理学—数学]