On skew-cyclic codes over GR(4, 2) + uGR(4, 2)

Abstract

In this paper, we study skew-cyclic codes over the ring R = GR(4, 2) + uGR(4, 2), u2 = u, where GR(4, 2) is the Galois extension of ℤ4 of degree 2. We describe some structural properties of skew polynomial ring R[x, θ], where θ is an automorphism of R. A sufficient condition for skew cyclic codes over R to be free is presented. It is shown that skew-cyclic codes over R are either equivalent to cyclic codes or to quasi-cyclic codes. A brief description of the duals of these codes is also presented. We define a Gray map from R to [GR(4, 2)]2, and show that the Gray image of a skew-cyclic codes over R is a skew 2-quasi cyclic code over GR(4, 2).