Skew cyclic codes over Z4+uZ4+vZ4

In this paper, we study the skew-cyclic codes (also called θ -cyclic codes) over the ring S = Z 4 + u Z 4 + v Z 4 , where u 2 = v 2 = u v = v u = 0 . Some structural properties of the skew polynomial ring S [ x , θ ] , where θ is an automorphism of S are discussed and the elements of S θ , the subring of S fixed by θ , are determined. Skew cyclic codes over S are viewed as left S [ x , θ ] -submodules. Generator and parity-check matrices of a free θ -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 .