Partial flocks of the quadratic cone yielding Mathon maximal arcs

In [6] Hamilton and Thas (2006) describe a link between maximal arcs of Mathon type and partial flocks of the quadratic cone. This link is of a rather algebraic nature. In this paper we establish a geometric connection between these two structures. We also define a composition on the flock planes an...

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Bibliographic Details
Published in:Discrete mathematics 2012-08, Vol.312 (16), p.2421-2428
Main Authors: De Clerck, F., De Winter, S., Maes, T.
Format: Article
Language:English
Subjects:
Algebra
Analogue
Construction
Hyperovals
Joints
Links
Mathematical analysis
Maximal arcs
Planes
Theorems
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Summary:In [6] Hamilton and Thas (2006) describe a link between maximal arcs of Mathon type and partial flocks of the quadratic cone. This link is of a rather algebraic nature. In this paper we establish a geometric connection between these two structures. We also define a composition on the flock planes and use this to work out an analogue of the synthetic version of Mathon’s theorem (see De Clerck et al. (2011) [3]). Finally, we show how it is possible to construct a maximal arc of Mathon type of degree 2d, containing a Denniston arc of degree d provided that there is a solution to a certain given system of trace conditions.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.04.028