01150631

j

01150631 Cusick, Thomas W. Value sets of some polynomials over finite fields. SIAM J. Comput. 27, No.1, 120-131 (1998). 1998 Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA EN finite field polynomial value set

doi:10.1137/S0097539794270352

Summary: 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 $\text{GF}(2^{2m})$. In particular, the size of such value sets is determined by using finite field theory and known results about crosscorrelation functions.