Geodesic
Low-degree planar monomials in characteristic two
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 695-699.

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Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They exist only in odd characteristic, but recently Zhou introduced an even characteristic analogue which has similar applications. In this paper we determine all planar functions on $\mathbb F_q$ of the form $c\mapsto ac^t$, where $q$ is a power of $2$, $t$ is an integer with $0$, and $a\in\mathbb F_q^\ast$. This settles and sharpens a conjecture of Schmidt and Zhou.
Classification : 51E20, 11T06, 11T71, 05B05
Keywords: planar function, projective plane, monomial functions 
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     author = {M\"uller, Peter and Zieve, Michael E.},
     title = {Low-degree planar monomials in characteristic two},
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Müller, Peter; Zieve, Michael E. Low-degree planar monomials in characteristic two. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 695-699. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a10/