Partial flocks of the quadratic cone yielding Mathon maximal arcs

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• 作者：F. De Clerck^a ; ^{fdc@cage.UGent.be} ; S. De Winter^b ; ^{sgdwinte@me.com} ; T. Maes^a ; ^{tmmaes@cage.ugent.be}
• 关键词：Maximal arcs ; Hyperovals
• 刊名：Discrete Mathematics
• 出版年：2012
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：28 August, 2012
• 卷：312
• 期：16
• 页码：2421-2428
• 文件大小：224 K

摘要

In聽 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鈥檚 theorem (see聽De Clerck et聽al. (2011)聽). Finally, we show how it is possible to construct a maximal arc of Mathon type of degree , containing a Denniston arc of degree provided that there is a solution to a certain given system of trace conditions.