Abstract
We discuss the problem of classifying Dembowski–Ostrom polynomials from the composition of reversed Dickson polynomials of arbitrary kind and monomials over finite fields of odd characteristic. 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 all such Dembowski–Ostrom polynomials. Planar Dembowski–Ostrom polynomials have applications in many areas including cryptography and coding theory.
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