Abstract
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.
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