环F_2+uF_2+u^2F_2上的线性码及其Gray像

Linear codes over F_2+uF_2+u^2F_2 and their Gray images

记R=F2+uF2+u2F2,R1=F2+uF2,定义了从Rn到F23n的Gray映射准以及从Rn1到Rn的映射f。通过对环R上线性码C的生成矩阵的研究,给出了线性码C的对偶码C⊥和Gray像准(C)的生成矩阵,并且准(C)与准(C⊥)是F2上的对偶码。通过映射f将环R1上的线性码与环R上的一类线性码对应起来。

Let R=F2＋uF2＋u2F2 and R1 =F2 ＋uF2,the Gray map φ from Rn to F23n and the map f from R1n to Rn are defined.By using the generator matrix of linear codes C over R,the generator matrices of the dual codes C⊥ and the Gray images φ（C） of the linear codes C are given,and the linear codes φ（C⊥） are the dual codes of φ（C） over F2.By the map f,linear codes over R1 are correspond to a class of linear codes over R.