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