MacWilliams Identities of Linear Codes Over Ring Z_4 with Respect to the RT Metric
Minjia Shi · Dianzi xuebao · 2009
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.