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Maximal arcs in PG(2, q ) and partial flocks of the quadratic cone

Maximal arcs in PG(2, q ) and partial flocks of the quadratic cone Abstract In this paper we show that there are several other structures that arise from the functions associated with the maximal arcs of Mathon type. So it is shown that maximal arcs of Mathon type are equivalent to additive partial flocks of the quadratic cone in PG(3, q ) and to additive partial q -clans. Further they yield partial ovoids of Q + (5, q ) partial spreads of lines of PG(3, q ), translation k -arcs of PG(2, q ) and m -ovoids of a certain classical generalized quadrangle. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Maximal arcs in PG(2, q ) and partial flocks of the quadratic cone

Hamilton, N; Thas, J. A
Advances in Geometry , Volume 6 (1) – Jan 26, 2006
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Publisher
de Gruyter
Copyright
Copyright © 2006 by the
ISSN
1615-715X
eISSN
1615-7168
DOI
10.1515/ADVGEOM.2006.003
Publisher site
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Abstract

Abstract In this paper we show that there are several other structures that arise from the functions associated with the maximal arcs of Mathon type. So it is shown that maximal arcs of Mathon type are equivalent to additive partial flocks of the quadratic cone in PG(3, q ) and to additive partial q -clans. Further they yield partial ovoids of Q + (5, q ) partial spreads of lines of PG(3, q ), translation k -arcs of PG(2, q ) and m -ovoids of a certain classical generalized quadrangle.

Journal

Advances in Geometry – de Gruyter

Published: Jan 26, 2006

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