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.
orthogonal dual hyperoval symplectic spread orthogonal spread