As the title suggests, I am trying to compute the DFT transform (over a finite field) of a function f: F_q^{n} -> R using the fftw3 library for C++.
The DFT formula in this case is:
X[a] = sum f(x) \omega ^ { - <a , x>}
Where \omega is the q-th root of unity, the dot-product is defined over the finite field.
The default computation using fftw3 is for complex values, and also omega is replaced by e^{-2pi* i /N} where N is the size of the input (evaluation of f).
I tried to look at the fftw3 documentation but DFT over finite fields are not mentioned. Asking ChatGPT led to nowhere. I tried to run some simple example with the fftw library using the fftw_plan_dft_1d call but it seems like there is no way to specify that I am working on a finite field. Any suggestion on how to modify the code or another dedicated library is appreciated. Thanks.