Translation hyperovals and $\mathbb{F}_2$-linear sets of pseudoregulus type

Jozefien D'haeseleer; Geertrui Van de Voorde

Translation hyperovals and $\mathbb{F}_2$-linear sets of pseudoregulus type

Combinatorics 2019-06-12 v1

Authors: Jozefien D'haeseleer , Geertrui Van de Voorde

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 Andr\'e/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 $\mathbb{F}_2$ -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 $(2,q^2)$ .

Cite

@article{arxiv.1906.04537,
  title  = {Translation hyperovals and $\mathbb{F}_2$-linear sets of pseudoregulus type},
  author = {Jozefien D'haeseleer and Geertrui Van de Voorde},
  journal= {arXiv preprint arXiv:1906.04537},
  year   = {2019}
}

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