Projections in vector spaces over finite fields

We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional projections via projections of random sets. In the end we study the projections of sets which have the (discrete) Fourier decay.
Comment: 14 pages, no figures, some typos were fixed, last version, to appear in Ann. Acad. Sci. Fenn. Math