Mappings of group shifts

A group shift is a proper closed shift-invariant subgroup ofG ^ℤ ₂ whereG is a finite group. We consider a class of group shifts in whichG is a finite field and show that mixing is a necessary and sufficient condition on such a group shift for all codes from it into another group shift to be affine and all codes from another group shift into it to be affine. As a corollary, it will follow forG=ℤ _p that two mixing group shifts are topologically conjugate if and only if they are equal.