Efficient computation of quaternary fixed polarity Reed-Muller expansions

A new fast algorithm for constructing the whole polarity coefficient matrices of fixed polarity Reed-Muller expansions over Galois Field GF(4) has been introduced. The matrices are generated in a recursive way making the algorithm computationally very effective in terms of basic field operations. The number of required additions and multiplications is advantageous when compared to the known Green´s algorithms. It is also possible to generate fixed polarity quaternary Reed-Muller expansion in some chosen polarity without the necessity of going through all the steps and recursions of the full algorithm. Fast flow diagrams for implementation of the new algorithms in hardware have also been shown