Reversibility is one of the most important characteristics of microscopic mechanisms in physics. It is our aim in this paper to describe some classes of linear cellular automata(LCAs) that can be studied in terms of an associated reversibleLCA. We prove that any given LCA having as local transition map a row contraction can be dilated to a LCA having a local rule with isometric components. We finally show that a LCAsuch that its global transition function is a partial isometry has a quantum LCA power dilation which is reversible.