Ternary Reed-Muller switching functions with fixed and mixed polarities

Abstract

The representation of ternary switching functions by means of Reed-Muller algebraic expansions described over the Galois field GF(3) is considered. An investigation of the structure of the various fixed polarity transforms leads to an evaluation of the computational cost of performing these manipulations. The existence of a large number of consistent mixed polarity canonical forms is demonstrated and their basis vectors and transforms are isolated.