A class of constacyclic codes and skew constacyclic codes over Z2s+uZ2s and their gray images

Abstract

In this paper, we study (1 + 2 s-1u) -constacyclic codes and a class of skew (1 + 2 s-1u) -constacyclic codes of odd length over the ring R=Z2s+uZ2s, u2= 0 , where s≥ 3 is an odd integer. We have obtained the algebraic structure of (1 + 2 s-1u) -constacyclic codes over R. Three new Gray maps from R to Z2+ uZ2 have been defined and it is shown that Gray images of (1 + 2 s-1u) -constacyclic codes and skew (1 + 2 s-1u) -constacyclic codes are cyclic codes, quasi-cyclic codes or codes that are permutation equivalent to quasi-cyclic codes over Z2+ uZ2. Using Magma, some good cyclic codes of length 6 over Z2+ uZ2 are obtained. © 2020, Korean Society for Informatics and Computational Applied Mathematics.