Classification of ovals and hyperovals in even order

Classify all ovals and hyperovals in the projective plane PG(2, q) for even q.

Background

The paper distinguishes ovals, which are (q + 1)-arcs, from hyperovals, which are (q + 2)-arcs when q is even. Although every oval in odd characteristic is a non-singular conic, even characteristic admits many ovals and hyperovals that are not conics, including examples derived from conics and the broader family of hyperovals. A complete classification for even q is explicitly left unresolved.