Constacyclic and cyclic codes over F-2 + uF(2) + u(2)F(2)
A new Gray map between codes over F-2 + uF(2) + u(2)F(2) and codes over F-2 is defined. We prove that the Gray image of a linear (1 - u(2))- cyclic code over F-2 + uF(2) + u(2)F(2) 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 F-2 + uF(2) + u(2)F(2) of length n is equivalent to a quasi-cyclic code.
cyclic code gray map quasi-cyclic code constacyclic code