5 research outputs found
A geometric approach to Mathon maximal arcs
In 1969 Denniston gave a construction of maximal arcs of degree d in
Desarguesian projective planes of even order q, for all d dividing q. In 2002
Mathon gave a construction method generalizing the one of Denniston. We will
give a new geometric approach to these maximal arcs. This will allow us to
count the number of isomorphism classes of Mathon maximal arcs of degree 8 in
PG(2,2^h), h prime.Comment: 20 page
On Mathon's construction of maximal arcs in Desarguesian planes. II
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 and
, the largest of a non-Denniston maximal arc of degree 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 and ,
then the largest of a non-Denniston maximal arc of degree in
PG(2,2^m) generated by a {p,q}-map is either \floor {m/2} +1 or \floor{m/2}
+2.Comment: 21 page