Orthogonal Dual Hyperovals, Symplectic Spreads and Orthogonal Spreads

Orthogonal spreads in orthogonal spaces of type $V^+(2n+2,2)$ produce large numbers of rank $n$ dual hyperovals in orthogonal spaces of type $V^+(2n,2)$. The construction resembles the method for obtaining symplectic spreads in $V(2n,q)$ from orthogonal spreads in $V^+(2n+2,q)$ when $q$ is even.

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