SOME PLANAR MONOMIALS IN CHARACTERISTIC 2
Zachary Scherr, Michael, E. Zieve · 2015
Abstract. Planar functions over finite fields give rise to finite pro-jective planes and other combinatorial objects. They were originally defined only in odd characteristic, but recently Zhou introduced a def-inition in even characteristic which yields similar applications. In this paper we show that certain functions over F2r are planar, which proves a conjecture of Schmidt and Zhou. The key to our proof is a new result about the Fq3-rational points on the curve xq−1 + yq−1 = zq−1. 1.