A new algorithm to compute quaternary Reed-Muller expansions

Abstract

A new algorithm to construct a full polarity matrix for n-variable quaternary Reed-Muller expansions has been introduced. The new algorithm directly utilizes the truth vector of the function to construct the polarity matrix. The computational complexity of the algorithm is analyzed and compared with other existing algorithms. It is shown that for n/spl les/6, the new algorithm is computationally more efficient than all existing algorithms. Finally the fast flow diagram which is useful for implementation of the algorithm in hardware has also been shown.