Gray images of (1 - u)-constacyclic codes over the ring F-pk

Let R-u2, (v2), (pk) = F-pk + uF(pk) + vF(pk) + uvF(p)(,)(k) where u(2) = 0, v(2) = 0, uv = vu, p is a prime and k is a positive integer. We define a gray map from a linear code of length n over the ring R-u2, (v2), (pk) to a linear code of length p(2k)n over the field F-pk. In this paper, we characterize the gray images of (1-u)-constacyclic codes of an arbitrary length over the ring R-u2, (v2), (pk) in terms of quasicyclic codes over F-pk. We obtain some optimal linear codes over F-4 as gray images.