Dembowski-Ostrom polynomials from Dickson polynomials

Motivated by several recent results, we determine precisely when F"k(X^d,a)-F"k(0,a) is a Dembowski-Ostrom polynomial, where F"k(X,a) is a Dickson polynomial of the first or second kind. As a consequence, we obtain a classification of all such polynomials which are also planar; all examples found are equivalent to previously known examples.

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