Partial flocks of the quadratic cone yielding Mathon maximal arcs

Details Partial flocks of the quadratic cone yielding Mathon maximal arcs Partial flocks of the quadratic cone yielding Mathon maximal arcs

2011-10-07

arxiv.org/abs/1110.1667v1

Mathematics

Combinatorics

Scientific paper

N. Hamilton and J. A. Thas 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. 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.

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