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Planar arcs

Author
Ball, S.; Lavrauw, M.
Type of activity
Journal article
Journal
Journal of combinatorial theory. Series A
Date of publication
2018-11-01
Volume
160
First page
261
Last page
287
DOI
https://doi.org/10.1016/j.jcta.2018.06.015 Open in new window
Project funding
Discrete, geometric and random structures
Repository
http://hdl.handle.net/2117/125122 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S0097316518300955 Open in new window
Abstract
Let p denote the characteristic of , the finite field with q elements. We prove that if q is odd then an arc of size in the projective plane over , which is not contained in a conic, is contained in the intersection of two curves, which do not share a common component, and have degree at most , provided a certain technical condition on t is satisfied. This implies that if q is odd then an arc of size at least is contained in a conic if q is square and an arc of size at least is contained in a co...
Citation
Ball, S., Lavrauw, M. Planar arcs. "Journal of combinatorial theory. Series A", 1 Novembre 2018, vol. 160, p. 261-287.
Keywords
Galois geometry, MDS conjecture, Singleton hound, algebraic curves, arcs, finite geometry, linear codes, projective geometry
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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