Recursive Evaluation of the Generalized Reed-Muller Coefficients

초록

Abstract :In this paper, we propose the computation method of GRM(Generalized Reed - Muller) coefficients over GF(2) using triangle cell recursively. GRM expansions of each polarity contain different numbers of product terms. Hence, the minimum form may be selected from them. Many authors have presented various algorithms of calculating the coefficients of GRM expansions under mixed polarities. The method proposed by W. Besslich requires modulo - sums(i.e. Ex-OR)[1], but the method proposed in this paper requires only (the number of modulo-sums for n-1 variable)ones. From this proposed method we can get easily GRM coefficients.