Some Results on the Linear Codes over the Finite Ring F 2 + V 1 F 2 + ⋯ + V R F 2

Abstract

In this paper, we study the structure of cyclic, quasi-cyclic codes and their skew codes over the finite ring Br=F2+v1F2+⋯+vrF2, vi2=vi,vivj=vjvi=0,1≤i,j≤r for r≥1. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic codes over Br are obtained. A necessary and sufficient condition for cyclic code over Br that contains its dual has been given. The parameters of quantum error correcting codes are obtained from cyclic codes over Br. © 2016 World Scientific Publishing Company.