(1+ϑ)-constacyclic codes over Z8 +ϑZ8

Abstract

In this paper, (1+ϑ)-constacyclic codes of arbitrary length m over a non-chain finite local frobenious ring Z₈ + ϑZ₈ are introduced. A new Gray map is constructed from Z₈ + ϑZ₈ to Z₈⁸ and proved that the Z₈ - Gray image of (1+ϑ)-constacyclic codes having prescribed length m over the ring Z₈ +ϑZ₈ is a cyclic code of length 8m over the ring Z₈. Moreover, it has been obtained that the binary image of the (1+ϑ)-constacyclic code of length m over Z₈ +ϑZ₈ is a distance invariant binary quasi-cyclic code of length 32m with index 16.