Skew cyclic codes over Z4 + uZ4 + vZ4

Abstract

In this paper, we study the skew-cyclic codes (also called ?-cyclic codes) over the ring S = Z(4) + uZ(4) + vZ(4), where u(2) = v(2) = uv = vu = 0. Some structural properties of the skew polynomial ring S[x, ?], where ? is an automorphism of S are discussed and the elements of S-?, the subring of S fixed by ?, are determined. Skew cyclic codes over S are viewed as left S[x, ?]-submodules. Generator and parity-check matrices of a free ?-cyclic code of even length over S are determined and a Gray map on S is used to obtain the Z(4)- images. We show that the Gray image of a free skew cyclic code over S is a free linear code over Z(4). Furthermore, these codes are generalized to double skew-cyclic codes. We obtained new linear codes over Z(4) from Gray images of double skew-cyclic codes over S.