ON GRAY IMAGES OF CONSTACYCLIC CODES OVER THE FINITE RING F2 + u1 F2 + u2 F2

M. Özkan, A. Dertli, Y. Cengellenmis

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Abstract

We introduce the nite ring F2 + u1F2 + u2F2, u1 2 = u1 ; u2 2 = 0 ; u1:u2 = u2:u1 = 0 which is not a nite chain ring. We focus on (1 + u2) -constacyclic codes over F2 + u1F2 + u2F2 of odd length. We prove that the Gray image of a linear (1 + u2)-constacyclic code over F2 + u1F2 + u2F2 of odd length n is a quasi-cyclic code of index 4 and length 4n over F2.

Keywords

Constacylic code, Gray image.