环R+uR+vR+uvR上线性码的MacWilliams恒等式

MacWilliams Identities of Linear Codes over Ring R+uR+vR+uvR

针对环R+uR+vR+uvR(u^2=u,v^2=v,uv=vu)上的线性码,提出了在该环上各种重量的MacWilliams恒等式问题.通过构造Gray映射,对该环上线性码进行了研究.最后得到其对偶码的各种重量分布,为利用该环上线性码构造环R的剩余域上的码提供重要的理论依据.

Aiming at linear codes ring R+uR+vR+uvR(u^2=u,v^2=v,uv=vu),the MacWilliams identities of weight distributions on the ring are proposed.By constructing gray map,linear codes ring R+uR+vR+uvR are studied.According to these identities,the weight distributions of dual codes can be found.It is beneficial to construct the codes on the remaining domain of the ring R.