On the Bernoulli automorphism of reversible linear cellular automata

This investigation studies the ergodic properties of reversible linear cellular automata over ZmZm for m∈Nm∈N. We show that a reversible linear cellular automaton is either a Bernoulli automorphism or non-ergodic. This gives an affirmative answer to an open problem proposed by Pivato [20] for the case of reversible linear cellular automata.