ℤ4R-additive cyclic and constacyclic codes and MDSS codes

In this paper, we will study the structure of [Formula: see text]-additive codes where [Formula: see text] is the well-known ring of 4 elements and [Formula: see text] is the ring given by [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text]. We will classify all maximum distance separable codes with respect to the Singleton bound (MDSS) over [Formula: see text] Then we will focus on [Formula: see text]-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 [Formula: see text]-additive cyclic or constacyclic code.