New information on the effectiveness of different reed-muller algebras on the representation of quaternary functions

Abstract

Efforts to get reliable data about the efficiency of a set of basis functions in representing a Reed-Muller canonical form with the minimum number of coefficients are frustrated by the long computation times necessary for calculation. Using an integrated suite of utility programs employing fast transforms, we provide statistics on the performance of six different algebras for two, three, four and five variables. Based on experimental results we suggest that the choice of basis functions has only a marginal effect for random samples from the entire function space. In addition we provide evidence which suggests that providing additional polarities has a more and more marginal effect upon efficiency.