Linear codes over F_2+uF_2+u~2F_2 and their Gray images
Yuansheng Tang · Computer Engineering and Applications Journal · 2009
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.