A characterisation of translation ovals in finite even order planes

2013/05/29 by S. G. Barwick, Wen-Ai Jackson, Barwick, S. G. +1
Mathematics · #51E20 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:51E20

paper · pdf · doi:10.48550/arxiv.1305.6673

arxiv created 2013/05/29 · arxiv updated 2013/05/30

Abstract

In this article we consider a set C of points in PG(4,q), q even, satisfying certain combinatorial properties with respect to the planes of PG(4,q). We show that there is a regular spread in the hyperplane at infinity, such that in the corresponding Bruck-Bose plane PG(2,q²), the points corresponding to C form a translation hyperoval, and conversely.

Related

• Translation hyperovals and \mathbbF₂-linear sets of pseudoregulus type
• Characterising pointsets in PG(4,q) that correspond to conics
• On Translation Hyperovals in Semifield Planes
• A genealogy of the translation planes of order 25
• Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order