Cyclic Codes over Fp + uFp+ ··· +uk-1 Fp

SUMMARY The ring F p + uF p + · · · + u k−1 F p may be of interest in coding theory, which have already been used in the construction of optimal frequency-hopping sequence. In this work, cyclic codes over F p + uF p + · · ·+u k−1 F p which is an open problem posed in [1] are considered. Namely, the structure of cyclic code over F p + uF p + · · · + u k−1 F p and that of their duals are derived.