On double cyclic codes over Z2

Abstract

In this paper, we introduced double cyclic codes over Rr x Rs, where R = Z2 + uZ2 = {0, 1, u, 1 + u} is the ring with four elements and u2 = 0. We first determined the generator polynomials of R -double cyclic codes for odd integers r and s, then gave the generators of duals of free double cyclic codes over Rr x Rs. By defining a linear Gray map, we looked at the binary images of R -double cyclic codes and gave several examples of optimal parameter binary linear codes obtained from R -double cyclic codes. Moreover, we studied self -dual R -double cyclic codes and presented an example of a self -dual R -double cyclic code.