Constacyclic and Cyclic Codes over F2+uF2+u2F2

Jian-Fa QIAN  Li-Na ZHANG  Shi-Xin ZHU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.6   pp.1863-1865
Publication Date: 2006/06/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.6.1863
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
cyclic code,  constacyclic code,  quasi-cyclic code,  Gray map,  

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A new Gray map between codes over F2+uF2+u2F2 and codes over F2 is defined. We prove that the Gray image of a linear (1-u2)-cyclic code over F2+uF2+u2F2 of length n is a binary distance invariant linear quasi-cyclic code. We also prove that, if n is odd, then every binary code which is the Gray image of a linear cyclic code over F2+uF2+u2F2 of length n is equivalent to a quasi-cyclic code.