Spreads of T2(o), α-flocks and Ovals

M.R. Brown, C.M. O'Keefe, S.E. Payne, Tim Penttila, Gordon Royle

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)251-282
JournalDesigns Codes and Cryptography
Volume31
Issue number3
DOIs
Publication statusPublished - 2004

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