On the non--existence of certain hyperovals in dual Andr\'e planes of order $2^{2h}$

TL;DR

This paper proves that certain hyperovals in Desarguesian affine planes of order 2^{2h} do not extend to dual André planes of the same order, highlighting limitations in hyperoval inheritance.

Contribution

It establishes the non-existence of specific hyperovals in dual André planes derived from Desarguesian affine planes of order 2^{2h}.

Findings

No regular hyperoval of AG(2,2^{2h}) is inherited by dual André planes.

The result applies for all h > 1.

Highlights structural limitations in hyperoval inheritance.

Abstract

No regular hyperoval of the Desarguesian affine plane $AG(2,2^{2h})$, with $h>1$, is inherited by a dual Andr\'e plane of order $2^{2h}$ with dimension 2 over its centre.