AbuAlrub et al in (Des Codes Crypt 42:273-287, 2007) proposed an open problem in decoding of cyclic codes over the rings F2 + uF2 with u2 = 0: In this paper we resolve this open problem and extend this decoding procedure for cyclic codes of arbitrary length over the ring Fp[u] ⟨uk⟩ , where p is a prime number and uk = 0: Note that the ring Fp[u] ⟨uk⟩ = Fp + uFp + + uk1Fp may be of interest in coding theory, which have already been used in the construction of optimal frequency-hopping sequence.
