Skew cyclic codes over Z4

In this work, we study a class of skew cyclic codes over the ring R := Z4 + vZ4, where v2 = v, with an automorphism theta and a derivation Delta o, namely codes as modules over a skew polynomial ring R[x; theta, Delta o], whose multiplication is defined using an automorphism theta and a derivation Delta o. We investigate the structures of a skew polynomial ring R[x; theta, Delta o]. We define Delta o-cyclic codes as a generalization of the notion of cyclic codes. The properties of Delta o-cyclic codes as well as dual Delta o-cyclic codes are derived. As an application, some new linear codes over Z4 with good parameters are obtained by Plotkin sum construction, also via a Gray map as well as residue and torsion codes of these codes.