Singer 8-arcs of Mathon type in PG(2,2^7)
Combinatorics
2010-10-08 v1
Abstract
In a former paper the authors counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2,2^h), h not 7 and prime. In this paper 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.
Cite
@article{arxiv.1010.1279,
title = {Singer 8-arcs of Mathon type in PG(2,2^7)},
author = {Frank De Clerck and Stefaan De Winter and Thomas Maes},
journal= {arXiv preprint arXiv:1010.1279},
year = {2010}
}
Comments
13 pages