The parametric coding of indices of the Fourier matrix have been used to obtain the most efficient parametric decomposition of the Fourier matrix. Fast Fourier transform (FFT) is the most popular algorithm for processing discrete periodic signals. The general approach to constructing FFTs involves the decomposition of the Fourier matrix into a product of sparse matrices. Various versions of such decomposition depend on the arithmetic properties of the order of the Fourier matrix and on representations of its indices. A parametric version of the prime factor method with successive permutations was suggested. It was concluded that the corresponding FFT algorithm involves no complicated permutations of data before or after the transform, and computations can be performed simultaneously with permutations.