Duhamel/Hollmann-Like Discrete Fourier Transform Algorithm With the Smallest Multiplicative Complexity Over a Finite Field

The new method for the discrete Fourier transform computation over a finite field is introduced. This method is a nontrivial generalization of the Duhamel-Hollmann algorithm with replacement of the Toeplitz convolution calculation by the normalized cyclic convolution calculation. Both algorithms have the smallest multiplicative complexity.