New infinite families of hyperovals of the generalized quadrangle H(3, q2) are provided. They arise in different geometric contexts. More precisely, we construct hyperovals by means of certain subsets of the projective plane called here k-tangent arcs with respect to a Hermitian curve (Section 2), hyperovals arising from the geometry of an orthogonal polarity commuting with a unitary polarity (Section 3), hyperovals admitting the irreducible linear group PSL(2,7) as a subgroup of PGU(3,q2), q=ph, p≡3,5or6(mod7) and h an odd integer (Section 4). Finally we construct hyperovals by means of the embedding of PSp(4,q)<PGU(4,q2) as a subfield subgroup (Section 5). © 2013 Elsevier Inc.
Hyperoval constructions on the Hermitian surface / Cossidente, Antonio; Pavese, Francesco. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 25:(2014), pp. 19-25. [10.1016/j.ffa.2013.07.008]
Hyperoval constructions on the Hermitian surface
PAVESE, Francesco
2014-01-01
Abstract
New infinite families of hyperovals of the generalized quadrangle H(3, q2) are provided. They arise in different geometric contexts. More precisely, we construct hyperovals by means of certain subsets of the projective plane called here k-tangent arcs with respect to a Hermitian curve (Section 2), hyperovals arising from the geometry of an orthogonal polarity commuting with a unitary polarity (Section 3), hyperovals admitting the irreducible linear group PSL(2,7) as a subgroup of PGU(3,q2), q=ph, p≡3,5or6(mod7) and h an odd integer (Section 4). Finally we construct hyperovals by means of the embedding of PSp(4,q)I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
