The use of finite fields to compute convolutions
I.S. Reed, Treiu-Kien Truong · IEEE Transactions on Information Theory · 1975
A transform is defined in the Galois field ofq^2elementsGF(q^2), a finite field analogous to the field of complex numbers, whenqis a prime such that (--1) is not a quadratic residue. It is shown that the action of this transform overGF(q^2)is equivalent to the discrete Fourier transform of a sequence of complex integers of finite dynamic range. Ifqis a Mersenne prime, one can utilize the fast Fourier transform (FFT) algorithm to yield a fast convolution without the usual roundoff problem of complex numbers.