DECODING OF CYCLIC CODES OVER THE RING Fp[u] ⟨uk⟩, By Mohammadreza Alimoradi

Research

Title	DECODING OF CYCLIC CODES OVER THE RING Fp[u] ⟨uk⟩
Type	JournalPaper
Keywords	Cyclic codes, Hamming distance, Decoding, Torsion codes, frequencyhopping sequence.
Year	2017
Journal	University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics
DOI
Researchers	Mohammadreza Alimoradi

Abstract

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 + + uk􀀀1Fp may be of interest in coding theory, which have already been used in the construction of optimal frequency-hopping sequence.