Characterization of the ergodicity of 1-Lipschitz functions on Z2Z2 using the q-Mahler basis

The ergodicity of 1-Lipschitz functions on Z2Z2 represented by the Mahler basis was characterized by V.S. Anashin (1994) in [1]. His results are mainly based on the so-called folklore criterion for ergodicity, depending on the algebraic normal form of Boolean functions associated with coordinate functions. In this paper, we employ the q-Mahler basis to provide q-analogues of Anashin's results whose proof does not rely on this criterion.