A Class of Constacyclic Codes over R + vR and Its Gray Image

Dajian Liao, Yuansheng Tang

College of Science, Huaihai Institute of Technology, Lianyungang, China.

DOI: 10.4236/ijcns.2012.54029                

Abstract

We study (1 + 2v)-constacyclic codes overR + vR and their Gray images, where v² + v = 0 and R is a finite chain ring with maximal ideal <λ> and nilpotency index e. It is proved that the Gray map images of a (1 + 2v)-constacyclic codes of length n over R + vR are distance-invariant linear cyclic codes of length 2n over R. The generator polynomials of this kind of codes for length n are determined, where n is relatively prime to p, p is the character of the field R/<λ> . Their dual codes are also discussed.

Keywords

Frobenius Ring; Constacyclic Codes; Generator Polynomial; Dual Codes

Conflicts of Interest

The authors declare no conflicts of interest.

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