Cyclic codes over F2 + uF2 + vF2 + uvF2 + u2F2 + v2F2 + u2v2F2

Mohammad A.M. Hamoda; Abd Elkarim Naji

Mohammad A.M. Hamoda Associate Prof. Department of Mathematics, Al-Aqsa University, Palestine
Abd Elkarim Naji Associate Prof. Department of Mathematics, Al-Aqsa University, Palestine

Keywords: Cyclic codes, Codes over rings, Gray map, Lee weight.

Abstract

In this paper, we study the structure of cyclic codes of length n over the ring

F2 +uF2 +vF2 +uvF2 +u2F2 +v2F2 +u2v2F2. We characterize a set of generators for each cyclic code. We study the rank for these codes, and we find their minimal spanning sets. Lee weights and Gray maps for these codes over F2 + uF2 + vF2 +uvF2 + u2F2 + v2F2 + u2v2F2 are also studied.

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