Abstract
A condition is found that determines whether a polynomial over GF(q) gives an oval in PG(2, q), q even. This shows that the set of all ovals of PG(2, q) corresponds to a certain variety of points of PG((q−4)/2, q). The condition improves upon that of Segre and Bartocci, who proved that all the terms of an oval polynomial have even degree. It is suitable for efficient computer searches.
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Glynn, D.G. A condition for the existence of ovals in PG(2, q), q even. Geom Dedicata 32, 247–252 (1989). https://doi.org/10.1007/BF00147433
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DOI: https://doi.org/10.1007/BF00147433