Dembowski–Ostrom polynomials and reversed Dickson polynomials

Dembowski-Ostrom polynomials and Dickson polynomials

“…This observation inspired Coulter and Matthews [7] to classify DO polynomials from Dickson polynomials of first and second kind over finite fields of odd characteristic. Recently, the authors along with Fernando [13] classified DO polynomials from the composition of reversed Dickson polynomials of arbitrary kind and monomials over finite fields of odd characteristic.…”

“…In continuation of our work in [13], we now consider the problem of classifying DO polynomials stemming from the Dickson polynomials of arbitrary kind over finite fields of odd characteristic. In fact, we give a complete classification of DO polynomials arising from the composition of Dickson polynomial of the (m + 1)-th kind (where m ≥ 2) and the monomial X d , where d is a positive integer, in odd characteristic.…”

“…Discussion on planarity. We shall first discuss some tools and techniques, also described in [13], required to handle planarity of the DO polynomials obtained in the previous sections and listed in Appendix A. As defined earlier, a function…”