Decoding of Cyclic Codes Over the Ring $$\frac{{{F_2}\left[ u \right]}}{{\langle {u^t}\rangle }}$$ F 2 [ u ] 〈 u t 〉

Karim Samei () and Mohammad Reza Alimoradi ()
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Karim Samei: Bu-Ali Sina university
Mohammad Reza Alimoradi: University of Malayer

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 113-120

Abstract: Abstract In this paper we resolve an open problem about decoding cyclic codes over the ring F2+uF2 with u2 = 0. This problem was first proposed by AbuAlrub et al. in (Des Codes Crypt 42: 273-287, 2007). Also we extend this decoding procedure for cyclic codes of arbitrary length over the ringe $$\frac{{{F_2}\left[ u \right]}}{{\langle {u^t}\rangle }} = {F_2} + u{F_2} + {u^2}{F_2} + \cdots {u^{t - 1}}{F_2}$$ F 2 [ u ] 〈 u t 〉 = F 2 + u F 2 + u 2 F 2 + ⋯ u t − 1 F 2 , where ut = 0.

Keywords: Cyclic codes; Hamming distance; decoding; torsion codes (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0310-2

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