Ergodicity of linear cellular automata over Z subscript m

The study of parallel maps is centrally located in cellular automata theory and has been discussed from various points of view. Wilson (1975) regarded the set of all configurations as a probability space and introduced measure-preserving parallel maps and gave a sufficient condition for a parallel map to be ergodic. Attention is restricted to linear cellular automata over Z subscript m, and the necessary sufficient conditions are given for a parallel to map to be ergodic. As a result, it is shown that the problem of whether or not a linear parallel map is ergodic is decidable.