TY - JOUR
T1 - Triads, flocks of conics and Q-(5,q),
AU - Brown, M.R.
AU - O'Keefe, C.M.
AU - Penttila, Tim
PY - 1999
Y1 - 1999
N2 - 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, which admits a flock of conics must be an elliptic quadric. This latter result is used to give a characterisation of the classical example Q(-)(5,q) among 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 certain triads.
AB - 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, which admits a flock of conics must be an elliptic quadric. This latter result is used to give a characterisation of the classical example Q(-)(5,q) among 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 certain triads.
U2 - 10.1023/A:1008376900914
DO - 10.1023/A:1008376900914
M3 - Article
SN - 0925-1022
VL - 18
SP - 63
EP - 70
JO - Designs Codes and Cryptography
JF - Designs Codes and Cryptography
ER -