Dembowski-Ostrom polynomials and Dickson polynomials

Abstract

We give a complete classification of Dembowski-Ostrom polynomials from the composition of Dickson polynomials of arbitrary kind and monomials over finite fields. Moreover, by using a variant of the Weil bound for the number of points of affine algebraic curves over finite fields, we discuss the planarity of the obtained Dembowski-Ostrom polynomials. Dembowski-Ostrom polynomials play a crucial role in coding theory and cryptography.