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 -