Bounds for arcs of arbitrary degree in finite desarguesian planes

Hirschfeld, J W P and Pichanick, E V D (2016) Bounds for arcs of arbitrary degree in finite desarguesian planes. Journal of Combinatorial Designs, 24 (4). pp. 184-196. ISSN 1063-8539

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Abstract

This paper examines subsets with at most n points on a line in the projective plane π q = PG(2, q). A lower bound for the size of complete (k, n)-arcs is established and shown to be a generalisation of a classical result by Barlotti. A sufficient condition ensuring that the trisecants to a complete (k, 3)-arc form a blocking set B in the dual plane π∗ q is provided. Finally, combinatorial arguments are used to show that, for q ≥ 17, plane (k, 3)-arcs satisfying a prescribed incidence condition do not attain the best known upper bound.

Item Type: Article
Keywords: finite projective planes; complete arcs; elliptic curves
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science
Q Science > QA Mathematics
Depositing User: Sinead Rance
Date Deposited: 15 Dec 2015 15:37
Last Modified: 08 Mar 2017 05:49
URI: http://sro.sussex.ac.uk/id/eprint/58843

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