Abstract
Let [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] is a prime and [Formula: see text] is a positive integer. We define a gray map from a linear code of length [Formula: see text] over the ring [Formula: see text] to a linear code of length [Formula: see text] over the field [Formula: see text]. In this paper, we characterize the gray images of [Formula: see text]-constacyclic codes of an arbitrary length over the ring [Formula: see text] in terms of quasicyclic codes over [Formula: see text]. We obtain some optimal linear codes over [Formula: see text] as gray images.
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