环Mn×s(Rk)上线性码关于RT距离的MacWilliams恒等式

MacWilliams identities of linear codes over Mn×s(Rk) with respect to RT metric

摘要: 定义了环Mn×s(Rk)(u2i=0,uiuj=ujui)上线性码的Lee完全ρ重量计数器和精确完全ρ重量计数器,并给出了环Mn×s(Rk)上线性码关于这两种重量计数器的MacWilliams恒等式.最后给出两个例子对所得的结果进行了验证.

Abstract: The definitions of the Lee complete ρ weight enumerator and the exact complete ρ weight enumerator over Mn×s(Rk)(u2i=0,uiuj=ujui) were given, and the MacWilliams identities with respect to the RT metric for these two weight enumerators of linear codes over Mn×s(Rk) were obtained, respectively. Finally, two examples were presented to illustrate our obtained results.