环Z4上线性码关于RT距离的MacWilliams恒等式

 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.

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

There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (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 identities,to obtain the dual code C^⊥ of the Z₄-linear code C,we can get the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator of the dual code C ⊥ directly.