On the Gray Image of Cyclic Codes over Finite Chain Rings

Jianfa QIAN
Wenping MA
Xinmei WANG

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.9    pp.2685-2687
Publication Date: 2008/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.9.2685
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
(1-γ)-cyclic code,  Gray map,  quasi-cyclic code,  cyclic code,  

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We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over Fpk. We also prove that if (n,p)=1, then every code over Fpk which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.