On Mathon's construction of maximal arcs in Desarguesian planes. II

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dc.creatorFiedler, Frank
dc.creatorLeung, Ka Hin
dc.creatorXiang, Qing
dc.date2004-01-05
dc.date.accessioned2026-07-07T05:04:22Z
dc.date.available2026-07-07T05:04:22Z
dc.descriptionIn a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when $m\geq 5$ and $m\neq 9$, the largest $d$ of a non-Denniston maximal arc of degree $2^d$ in PG(2,2^m) generated by a {p,1}-map is $(\floor {m/2} +1)$. This confirms our conjecture in [FLX]. For {p,q}-maps, we prove that if $m\geq 7$ and $m\neq 9$, then the largest $d$ of a non-Denniston maximal arc of degree $2^d$ in PG(2,2^m) generated by a {p,q}-map is either $\floor {m/2} +1$ or $\floor{m/2} +2$.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0401030
dc.identifierhttp://arxiv.org/abs/math/0401030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69775
dc.subjectCombinatorics
dc.subject51E21; 51E05
dc.titleOn Mathon's construction of maximal arcs in Desarguesian planes. II
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