Translation hyperovals and \mathbbF₂-linear sets of pseudoregulus type

2019/06/11 by D'haeseleer, Jozefien, Van de Voorde, Geertrui
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.04537

Abstract

In this paper, we study translation hyperovals in PG(2,q^k). The main result of this paper characterises the point sets defined by translation hyperovals in the André/Bruck-Bose representation. We show that the affine point sets of translation hyperovals in PG(2,q^k) are precisely those that have a scattered \mathbbF₂-linear set of pseudoregulus type in PG(2k-1,q) as set of directions. This correspondence is used to generalise the results of Barwick and Jackson who provided a characterisation for translation hyperovals in PG(2,q²).

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