On (1− u) -cyclic codes over [formula omitted

Abstract

We extend the results of [J.F. Qian, L.N. Zhang, S.X. Zhu, ( 1 + u ) -constacyclic and cyclic codes over F 2 + u F 2 , Appl. Math. Lett. 19 (2006) 820–823. [3]] to codes over the commutative ring R = F p k + u F p k , where p is prime, k ∈ N and u 2 = 0 . In particular, we prove that the Gray image of a linear ( 1 − 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 .