Efficient algorithm for the generation of fixed polarity quaternary Reed-Muller expansions

An efficient algorithm for the generation of fixed polarity Reed-Muller expansions over Galois field GF(4) has been introduced. The polarity coefficient matrices of quaternary switching functions in Reed-Muller expansions are generated by means of recursive square matrices. The number of required addition and multiplication operations has been found advantageous in comparison to the known D.H. Green's (199) algorithm. Fast flow diagram allowing implementation of the new algorithm in hardware has also been presented.