ON GRAY IMAGES OF CONSTACYCLIC CODES OVER THE FINITE RING F-2 + u(1)F(2) + u(2)F(2)

Abstract

We introduce the finite ring F-2 + u(1)F(2) + u(2)F(2), u(1)(2) = u(1), u(2)(2) = 0, u(1).u(2) = u(2).u(1) = 0 which is not a finite chain ring. We focus on (1 + u(2)) -constacyclic codes over F-2 + u(1)F(2) + u(2)F(2) of odd length. We prove that the Gray image of a linear (1 + u(2)) -constacyclic code over F-2 + u(1)F(2) + u(2)F(2) of odd length n is a quasi-cyclic code of index 4 and length 4 n over F-2.