On $d$-dimensional dual hyperovals in $\mathsf{PG}(2d,2)$

Abstract

We show that $d$-dimensional dual hyperovals in $PG\left(2d,2\right)$ constructed from a regular nearfield of characteristic $2$ are not isomorphic to Yoshiara’s $d$-dimensional dual hyperovals in $PG\left(2d,2\right)$ constructed by Yoshiara. Thus we show that, in Cooperstein–Thas’s family, there exist non-isomorphic dual hyperovals.