MacWilliams Identities of Linear Codes with Respect to RT Metric over Mn×s(F2[u,v]/<uk,v2,uv-vu>)

Minjia SHI  Jie TANG  Maorong GE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.11   pp.2522-2527
Publication Date: 2017/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.2522
Type of Manuscript: LETTER
Category: Coding Theory
RT metric,  weight enumerator,  MacWilliams identities,  dual code,  

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The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over Mn×s(F2[u,v]/<uk,v2,uv-vu>) are introduced, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over Mn×s(F2[u,v]/<uk,v2,uv-vu>) are obtained. Finally, we give two examples to illustrate the results we obtained.