Classes of polynomial and variative coordinate polynomial functions over Galois ring

A new class of functions over Galois ring $R=\mathrm{GR}(q^m,p^m)$ named functions with the variative coordinate polynomiality (VCP-functions) is introduced. The relation between this class and the class of polynomial functions over $R$ is considered. An upper bound for the amount of such functions is presented, and sufficient conditions for a VCP-function not to be a polynomial are given.