Minimisation of Read-Muller Polynomials with Fixed Polarity

An efficient algorithm for minimisation of Reed–Muller polynomials with fixed polarities is presented. The common terms of multiple-output polynomials are considered by applying a number of logical operations on their coefficients. The minimisation of the polynomials over extension Galois fields GF(2M) is considered. The average number of field multiplications for mapping a set of coefficients is reduced to less than $$M \cdot 2^{M - 2}$$ M · 2 M - 2 .