Gray Images of Constacyclic Codes over a Non-chain Extension of Z 4

Let Formula: see text be the ring of integers modulo 4. We study the Formula: see text-constacyclic and Formula: see text-cyclic codes over the non-chain ring Formula: see text for a unit Formula: see text in Formula: see text. We define several Gray maps and find that the respective Gray images of a quasi-cyclic code over Formula: see text are cyclic, quasi-cyclic or permutation equivalent to this code. For an odd positive integer Formula: see text, we determine the generator polynomials of cyclic and Formula: see text-constacyclic codes of length Formula: see text over Formula: see text. Further, we prove that a Formula: see text-cyclic code of length Formula: see text is a Formula: see text-constacyclic code if Formula: see text is odd, and a Formula: see text-quasi-twisted code if Formula: see text is even. A few examples are also incorporated, in which two parameters are new and one is best known to date.