TY - JOUR
T1 - Spreads of T2(o), α-flocks and Ovals
AU - Brown, M.R.
AU - O'Keefe, C.M.
AU - Payne, S.E.
AU - Penttila, Tim
AU - Royle, Gordon
PY - 2004
Y1 - 2004
N2 - We establish a representation of a spread of the generalized quadrangle T 2(0), o an oval of PG(2, q), q even, in terms of a certain family of q ovals of PG(2, q) and investigate the properties of this representation. Using this representation we show that to every flock of a translation oval cone in PG(3, q) (-flock), q even, there corresponds a spread of T 2(o) for an oval o determined by the -flock. This gives constructions of new spreads of T 2(o), for certain ovals o, and in some cases solves the existence problem for spreads. It also provides a geometrical characterization of the ovals associated with a flock of a quadratic cone.
AB - We establish a representation of a spread of the generalized quadrangle T 2(0), o an oval of PG(2, q), q even, in terms of a certain family of q ovals of PG(2, q) and investigate the properties of this representation. Using this representation we show that to every flock of a translation oval cone in PG(3, q) (-flock), q even, there corresponds a spread of T 2(o) for an oval o determined by the -flock. This gives constructions of new spreads of T 2(o), for certain ovals o, and in some cases solves the existence problem for spreads. It also provides a geometrical characterization of the ovals associated with a flock of a quadratic cone.
U2 - 10.1023/B:DESI.0000015887.35146.14
DO - 10.1023/B:DESI.0000015887.35146.14
M3 - Article
SN - 0925-1022
VL - 31
SP - 251
EP - 282
JO - Designs Codes and Cryptography
JF - Designs Codes and Cryptography
IS - 3
ER -