On Translation Hyperovals in Semifield Planes
Combinatorics
2023-09-06 v1
Abstract
In this paper we demonstrate the first example of a finite translation plane which does not contain a translation hyperoval, disproving a conjecture of Cherowitzo. The counterexample is a semifield plane, specifically a Generalised Twisted Field plane, of order . We also relate this non-existence to the covering radius of two associated rank-metric codes, and the non-existence of scattered subspaces of maximum dimension with respect to the associated spread.
Cite
@article{arxiv.2309.01451,
title = {On Translation Hyperovals in Semifield Planes},
author = {Kevin Allen and John Sheekey},
journal= {arXiv preprint arXiv:2309.01451},
year = {2023}
}