最近,对由Rosenbloom和Tsfasman提出的码字的一个非Hamming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ID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上,即可得到C上的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.