Constacyclic and Cyclic Codes over F2 + uF2 + u2F2

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.