Recursive algorithm for generation of fixed polarity Reed-Muller expansions over GF(5)

This paper proposes a new algorithm for the optimization of five-valued functions using fixed polarity Reed-Muller expansions (FPRMEs). The algorithm is developed based on an optimized recursive definition of the FPRME polarity matrix over Galois field (5) and is advantageous over other algorithms when it is used to calculate a particular spectral coefficient vector. It also has the smallest computational cost of generating all the polarity matrix elements for some input functions. In this paper, the generation of the recursive definition of the polarity matrix that is used by the new algorithm is presented followed by the computational costs for the algorithm.