On Fixed Points and Cycles in the Reed Muller Domain

Abstract

This paper studies cycles that appear by repeatedly applying the RM transform to a p-valued function. It is shown that there are nontrivial fixed points, which correspond to eigenvectors of the transform and a simple method is proposed to determine the maximum period of n-place functions for a given p. The concept of spectral diversity is introduced, which may be applied to characterize p-valued functions.