Comparison of different features of quaternary Reed-Muller canonical forms and some new statistical results

An integrated set of utility programs in C is presented. These can be used to perform calculations in any quaternary Reed-Muller algebra by entering addition and multiplication tables, and the zero-polarity transform matrix. For every completely specified quaternary function, canonical forms are generated for any pre-selected set of polarities. A laboratory is used to generate statistics comparing the realisation efficiency of five different algebras. A number of optimisation statistics were generated and are discussed, and, based on our experiments, the number of non-zero coefficients in a representation seems to be a reasonable measure of complexity.