A class of skew-constacyclic codes over \(\mathbb{Z}_{4} + u \mathbb{Z}_{4}\) (Q725963)

Summary: In this paper, we study a class of skew-constacyclic codes over \(R = \mathbb{Z}_{4} + u\mathbb{Z}_{4}\), which is a non-chain extension of \(\mathbb{Z}_{4}\). Some structural properties of \(R[x, \theta]\) are discussed, where {\(\theta\)} is an automorphism of \(R\). We determine a necessary condition and a sufficient condition for these codes to be free, when they are principally generated. A Gray map over \(R\) is defined and some good codes are obtained using it. For even \(n\), a relation between the generator polynomial of a code and that of its dual is obtained. Some examples are given to illustrate the results. Further, we have generalised these codes to double skew-constacyclic codes over \(R\). Some good codes with improved minimum Lee distance over \(\mathbb{Z}_{4}\) have been found via this class, and the same have been added to the database of \(\mathbb{Z}_{4}\) codes.