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On planar arcs of size (q+3)/2

2021/05/23 by Günay, Gülizar, Lavrauw, Michel
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.10994

Abstract

The subject of this paper is the study of small complete arcs in PG(2,q), for q odd, with at least (q+1)/2 points on a conic. We give a short comprehensive proof of the completeness problem left open by Segre in his seminal work [20]. This gives an alternative to Pellegrino's long proof which was obtained in a series of papers in the 1980s. As a corollary of our analysis, we obtain a counterexample to a misconception in the literature [6].

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