On dual hyperovals of rank 4 over $${{\mathbb{F}}_2}$$ F 2

Abstract

We discuss dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\). In particular, we classify all such dual hyperovals if the ambient space has dimension 7 or 8. We also determine the bilinear dual hyperovals in the case of an ambient space of dimension 9 or 10. A classification of all dual hyperovals in dimension 9 seems possible in the near future.