A geometric approach to Mathon maximal arcs

TL;DR

This paper introduces a new geometric method to analyze Mathon maximal arcs in projective planes, enabling enumeration of isomorphism classes of degree 8 arcs in certain finite fields.

Contribution

It presents a novel geometric approach to Mathon maximal arcs, facilitating the counting of their isomorphism classes in specific finite projective planes.

Findings

Count of isomorphism classes of Mathon maximal arcs of degree 8 in PG(2,2^h) for prime h

New geometric framework for understanding maximal arcs

Extension of previous constructions by Denniston and Mathon

Abstract

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.