MACWILLIAMS IDENTITIES OVER $M_n\times_s(Z_4)$ WITH RESPECT TO THE RT METRIC
Shixin Zhu, Heqian Xu · Journal of applied mathematics & informatics · 2008
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 , in short). In this paper, the definitions of the Lee complete weight enumerator and the exact complete weight enumerator of a code over are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete weight enumerators of a linear code over are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over .