Exceptional planar polynomials

Florian Caullery; Kai-Uwe Schmidt; Yue Zhou

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arXiv · 1403.4015

Exceptional planar polynomials

Florian Caullery·Kai-Uwe Schmidt·Yue Zhou

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Abstract

Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many extensions of $K$; we call such polynomials exceptional planar. Exceptional planar monomials have been recently classified. In this paper we establish a partial classification of exceptional planar polynomials. This includes results for the classical planar functions on finite fields of odd characteristic and for the recently proposed planar functions on finite fields of characteristic two.

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Florian Caullery, Kai-Uwe Schmidt, Yue Zhou. 2014-03-17. Exceptional planar polynomials. https://arxiv.org/abs/1403.4015

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