On Mathon’s construction of maximal arcs in Desarguesian planes
نویسندگان
چکیده
We study the problem of determining the largest d of a non-Denniston maximal arc of degree 2 generated by a fp; 1g-map in PGð2; 2Þ via a recent construction of Mathon [9]. On one hand, we show that there are fp; 1g-maps that generate non-Denniston maximal arcs of degree 2ðmþ1Þ=2, where md 5 is odd. Together with Mathon’s result [9] in the m even case, this shows that there are always fp; 1g-maps generating non-Denniston maximal arcs of degree 2bðmþ2Þ=2c in PGð2; 2Þ. On the other hand, we prove that the largest degree of a non-Denniston maximal arc in PGð2; 2Þ constructed using a fp; 1g-map is less than or equal to 2 . We conjecture that this largest degree is actually 2bðmþ2Þ=2c when m > 9.
منابع مشابه
On Mathon’s Construction of Maximal Arcs in Desarguesian
In 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 ≥ 5 and m 6= 9, th...
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