On 2-dimensional dual hyperovals of polar type - Nakagawa, Nobuo (Utilitas Mathematica, 2008)
Exploiting an o-polynomial over GF(4), a direct proof is given for the fact that a 2-dimensional dual hyperoval S in PG(5, 4) of unitary polar type is isomorphic to the one exhibited in ([2] p.39). The proof provides enough automorphisms of S to conclude that Aut(S) ≅- M22.2. This gives an account for the exceptional embedding of the Mathieu group M22 into the unitary group PGU6(2) because the linear part of the automorphism group of a dimensional dual hyperoval of polar type is shown to preserve the associated form modulo the scalar multiplications (cf. Theorem 1).