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Translation hyperovals and F-2-linear sets of pseudoregulus type

Journal Contribution - Journal Article

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 Andre/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 F-2 -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, q(2)).
Journal: ELECTRONIC JOURNAL OF COMBINATORICS
ISSN: 1077-8926
Issue: 3
Volume: 27
Publication year:2020
Accessibility:Open