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Planar functions were introduced by Dembowski and Ostrom ([4]) to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a(More)
Several authors have recently shown that a planar function over a finite field of order q must have at least (q + 1)/2 distinct values. In this note this result is extended by weakening the hypothesis significantly and strengthening the conclusion. We also give an algorithm for determining whether a given bivariate polynomial φ(X, Y) can be written as f (X(More)
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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