Some properties of the discrete Fourier transform in the field of complex numbers and in the fields of finite characteristics

We consider the discrete Fourier transform over the field of complex numbers $C$ and over the Galois field $\mathrm{GF}(q)$. The length $N$ of a given vector over $C$ can be any positive integer, and in the Galois field $N$ is multiple to $(q-1)$. This imposes certain restrictions on possibilities for constructing Fast Fourier Algorithms in Galois fields and increases the dimension of input data.