Triads, flocks of conics and Q(-)(5,q)

Citation
Mr. Brown et al., Triads, flocks of conics and Q(-)(5,q), DES CODES C, 18(1-3), 1999, pp. 63-70
Citations number
15
Categorie Soggetti
Computer Science & Engineering
Journal title
DESIGNS CODES AND CRYPTOGRAPHY
ISSN journal
09251022 → ACNP
Volume
18
Issue
1-3
Year of publication
1999
Pages
63 - 70
Database
ISI
SICI code
0925-1022(199912)18:1-3<63:TFOCAQ>2.0.ZU;2-Z
Abstract
We show that if an ovoid of Q (4,q), q even, admits a flock of conics then that flock must be linear. It follows that an ovoid of PG (3,q), q even, wh ich admits a flock of conics must be an elliptic quadric. This latter resul t is used to give a characterisation of the classical example Q(-)(5,q) amo ng the generalized quadrangles T-3(O), where O is an ovoid of PG (3,q) and q is even, in terms of the geometric configuration of the centres of certai n triads.