Z4R-additive cyclic and constacyclic codes and MDSS codes

In this paper, we will study the structure of Z(4)R-additive codes where Z(4) = {0, 1, 2, 3} is the well-known ring of 4 elements and R is the ring given by R = Z(4) + uZ(4) + vZ(4), where u(2) = u, v(2) = v and uv = vu = 0. We will classify all maximum distance separable codes with respect to the Singleton bound (MDSS) over Z(4)R. Then we will focus on Z(4)R-additive cyclic and constacyclic codes. We will find a unique set of generator polynomials for these codes and determine minimum spanning sets for them. We will also find the generator polynomials for the dual of any Z(4)R-additive cyclic or constacyclic code.