On (1-u)-cyclic codes over Fpk + uFpk

We extend the results of [J.F. Qian, L.N. Zhang, S.X. Zhu, (1 + u)-constacyclic and cyclic codes over F-2 + uF(2), Appl. Math. Lett. 19 (2006) 820-823. [3]] to codes over the commutative ring R = F-p(k) + uF(p)(k), where p is prime, k epsilon N and u(2) = 0. In particular, we prove that the Gray image of a linear (t - u)-cyclic code over R of length n is a distance-invariant quasicyclic code of index p(k-1) and length p(k)n over F-p(k). We also prove that if (n, p) = 1, then every code of length p(k)n over F-p(k) which is the Gray image of a linear cyclic code of length n over R is permutation-equivalent to a quasicyclic code of index p(k-1).