Some Constacyclic and Cyclic Codes Over Fq[u]/<ut+1>

Reza SOBHANI  Morteza ESMAEILI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.4   pp.808-813
Publication Date: 2010/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.808
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
cyclic code,  constacyclic code,  quasi-cyclic code,  generalized Gray map,  generalized Necheav-Gray map,  

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Summary: 
A generalized Gray map for codes over the ring Fq[u]/<ut+1> is introduced, where q=pm is a prime power. It is shown that the generalized Gray image of a linear length-N (1-ut)-cyclic code over Fq[u]/<ut+1> is a distance-invariant linear length-qtN quasi-cyclic code of index qt/p over Fq. It turns out that if (N,p)=1 then every linear code over Fq that is the generalized Gray image of a length-N cyclic code over Fq[u]/<ut+1>, is also equivalent to a linear length-qtN quasi-cyclic code of index qt/p over Fq. The relationship between linear length-pN cyclic codes with (N,p)=1 over Fp and linear length-N cyclic codes over Fp+uFp is explicitly determined.