  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.

Number Theory