In 1969 Denniston [3] 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 [8] 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.

De Clerck et al. (J Comb Theory, 2011) counted the number of non-isomorphic Mathon maximal arcs of degree-8 in PG(2, 2 h ), h = 7 and prime. In this article we will show that in PG(2, 2 7 ) a special class of Mathon maximal arcs of degree-8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a detailed description of these arcs, and then count the total number of non-isomorphic Mathon maximal arcs of degree-8. Finally we show that the special arcs found in PG(2, 2 7 ) extend to two infinite families of Mathon arcs of degree-8 in PG(2, 2 k ), k odd and divisible by 7, while maintaining the nice property of admitting a Singer group.

In [6] 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 (see [3]). 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.