Optimal p-ary Codes from Constacyclic Codes over a Non-chain Ring R

This paper is devoted to the study of constacyclic codes over a non-chain ring R. The generator polynomials of all constacyclic codes over R are characterized and their dual codes are also determined. We also introduce a Gray map. It is proved that the image of a v-constacyclic code of length n over R under the Gray map is a cyclic code of length 2n over a field with p elements, where p is odd prime. Moreover, we obtain a substantial number of optimal p-ary linear (cyclic) codes, in terms of their parameters, via the Gray map.