Abstract
Some properties of arcs in PG(2,q) are discussed via its cyclic model. A covering number of a set χ of points in PG(2,q) is the smallest number of lines needed to cover the set -χ, where the set of points of PG(2,q) is identified with Z\(Z_{q^2 + q + 1} \). It is proved that the covering number of a conic is either 1 or greater than q/4. Hyperovals with covering number 2 are characterized for q even. Also, a possible method for constructing nonclassical hyperovals having small covering numbers is given.
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Kiss, G., Malnič, A. & Marušič, D. A New Approach to Arcs. Acta Mathematica Hungarica 84, 181–188 (1999). https://doi.org/10.1023/A:1006620816691
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DOI: https://doi.org/10.1023/A:1006620816691