Polynomials over base 2 finite fields with evenly distributed values

Few nontrivial results about the value sets of polynomials over finite fields are known. This paper uses results from the theory of crosscorrelation of binary m-sequences to find five kinds of polynomials f(x) defined over finite fields GF(2n) such that f(x) takes on each nonzero value only small a number of times (at most six times).