环Z_4上线性码关于RT距离的MacWilliams恒等式  

MacWilliams Identities of Linear Codes Over Ring Z_4 with Respect to the RT Metric

作　　者：朱士信[1] 许和乾[2] 施敏加[3] 

机构地区：[1]合肥工业大学数学系,安徽合肥230009 [2]合肥师范学院数学系,安徽合肥230601 [3]安徽大学数学科学学院,安徽合肥230601

出　　处：《电子学报》2009年第5期1115-1118,共4页Acta Electronica Sinica

基　　金：国家自然科学基金(No.60673074)

摘　　要：最近,对由Rosenbloom和Tsfasman提出的码字的一个非Hamming距离(简称为RT距离,或ρ距离)的研究引起了编码与密码学者的极大关注.本文定义并研究了Z4-码的Lee完全ρ重量计数器和精确完全ρ重量计数器,给出了Z4-线性码关于这两种ρ重量计数器相应的MacWilliams恒等式.利用该恒等式不必求出Z4-线性码C的对偶码C⊥,即可得到C⊥的Lee完全ρ重量计数器和精确完全ρ重量计数器.There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman melric （RT,or ρ ,in short）.In this paper, the definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator of codes over ring Z4 are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of linear codes over Z4 were proven respectively. It is not necessary, according to the identi- ties,to obtain the dual code C of the Z4-1inear code C,we can get the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator of the dual code C directly.

关 键 词：RT距离 重量计数器 MACWILLIAMS恒等式 线性码 对偶码 

分 类 号：TN911.22[电子电信—通信与信息系统]