The parallel algorithms of Fourier-Galois transforms synthesis in direct sums of finite rings

The method of fast algorithms of discrete transforms synthesis is considered. The algorithms synthesized with this method are the algorithms of "error-free" calculations of integer-valued discrete convolutions. The approach proposed in the paper is based on the following fact. The factorization of the elements in algebraic rings is can be performed in a number of ways. The choice of factorization is determined by the way in which the modular calculations are organized.