Gray images of (1 − u)-constacyclic codes over the ring 𝔽pk + u𝔽pk + v𝔽pk + uv𝔽pk

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.