On the Gray Image of Cyclic Codes over Finite Chain Rings

Jianfa QIAN; Wenping MA; Xinmei WANG

doi:10.1093/ietfec/e91-a.9.2685

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Online ISSN : 1745-1337
Print ISSN : 0916-8508

Regular Section

On the Gray Image of Cyclic Codes over Finite Chain Rings

Jianfa QIAN, Wenping MA, Xinmei WANG

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Keywords: (1-γ)-cyclic code, Gray map, quasi-cyclic code, cyclic code

JOURNAL RESTRICTED ACCESS

2008 Volume E91.A Issue 9 Pages 2685-2687

DOI https://doi.org/10.1093/ietfec/e91-a.9.2685

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Abstract

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 F_p^k. We also prove that if (n, p)=1, then every code over F_p^k which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.

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