环Fp^m+uFp^m+…+u^k-1Fp^m(u^k=0)上基于定义集的几类线性码  

Several Classes of Linear Codes from Defining Sets over Fp^m+uFp^m+…+u^k-1Fp^m(u^k=0)

作　　者：朱灿泽 方颖珏 廖群英 ZHU Canze;FANG Yingjue;LIAO Qunying(School of Mathematics and Statistics,Shenzhen University,Shenzhen,Guangdong,518060,P.R.China;School of Mathematical Sciences,Sichuan Normal University,Chengdu,Sichuan,610066,P.R.China)

机构地区：[1]深圳大学数学与统计学院,广东深圳518060 [2]四川师范大学数学科学学院,四川成都610066

出　　处：《数学进展》2020年第4期481-496,共16页Advances in Mathematics（China）

基　　金：NSFC(No.11601341);National Key Research and Development Program of China(No.2016QY04W0805)。

摘　　要：本文研究了有限链环Fp^m+uFp^m+…+u^k-1Fp^m(u^k=0)上基于定义集的线性码的李权重分布,其中p是奇素数,m,k是正整数.通过使用特征和工具,我们计算出上述线性码在Gray映射下的完备权重计数器.此外,还提出了一类满足Griesmer界的常数权重码,它可用于构造满足LVFC界限的最优常维码,本文推广了文献[IEEE Trans.Inf.Theory,2015,61(11):5835-5842]和[Des.Codes Cryptogr.,2019,87(1):15-29]的主要结果.In this paper,we study the Lee-weight distribution of linear codes from defining sets over the finite chain ringFp^m+uFp^m+…+u^k-1Fp^m(u^k=0),where p is an odd prime,m,k are positive integers.We establish the complete weight enumerator for the images of these linear codes under the Gray map explicitly by using character sums over finite fields.Furthermore,a class of constant weight codes achieving the Griesmer bound which can be used to construct optimal constant composition codes meeting the LVFC bound is obtained,which generalizes the main results in[IEEE Trans.Inf.Theory,2015,61(11):5835-5842]and[Des.Codes Cryptogr.,2019,87(1):15-29].

关 键 词：线性码 有限链环 完全权重计数器 特征和 

分 类 号：O157.4[理学—数学]