Reed-Muller variable-entered vectors and maps

Abstract

The technique of variable-entered maps is adapted to operate in the Reed-Muller regime where a range of different polarity maps is available. The related concept of the variable-entered vector is considered and shown to lead to reduced computational and storage costs when performing the many matrix transforms encountered in this area. This is of particular significance in the search for the optimum fixed or mixed polarity based on the successive generation of each form. The variable-entered versions of the extended truth vector also reduce the cost of deducing the minimum weight expansion using either a ternary map structure or in-place procedures on the vector itself. It is also demonstrated that variable-entered maps or vectors are useful when contemplating a synthesis by means of a modular circuit tree or when some form of simplification of exclusive-OR sums-of-products expressions is contemplated.