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 B-r = F-2 + v(1)F(2) + ... + v(r)F(2), v(i)(2) + v(i), v(i)v(j) = v(j)v(i) 0, 1 <= i, j <= r for r >= 1. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic codes over B-r 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 B-r.