Value Sets of Some Polynomials Over Finite Fields
Thomas W. Cusick · SIAM Journal on Computing · 1998
This paper shows that there is a connection between the crosscorrelation functions of certain binary m-sequences and the value sets of the polynomials x k (1 + x) 2 m - 1 for k in pm 1, pm 2, 4, where x is in the finite field GF(2 2m ). In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.