Z_（2~a）＋uZ_（2~a）上线性码的MacWilliams恒等式及自对偶码

Mac Williams identity and self-dual codes of linear codes over Z_（2~a）＋ uZ_（2~a）

考虑环R=Z2a+uZ2a上的线性码,其中u2=u。研究了环R上线性码的完全Gray权估计的M ac Williams恒等式。给出了环R上的自对偶码的生成矩阵及环Z23+u Z23上长为偶数n的自对偶码的数量公式。讨论了环R上的挠码,得到挠码的生成矩阵及挠码与剩余码的关系。

The linear codes over R = Z2 a＋ u Z2 awith u2= u are discussed. Mac Williams identity for the complete Gray weight enumerator is investigated firstly. Then,the generator matrices of self-dual codes over R and the number of distinct self-dual codes of even length n over Z23＋ u Z23 are given. The torsion codes over R are discussed and the generator matrices of torsion codes and the relationship between the torsion codes and the residue codes are also obtained.