A hyperoval in a finite projective plane of order 
is a set of 
points with
no three collinear. It can exist only when 
is even. In the projective
plane over 
,
hyperovals containing the two coordinate directions at infinity are described, after
affine normalization, by o-polynomials (Chen
and Huang 2026).
Hyperoval
See also
Finite Projective Plane, o-PolynomialExplore with Wolfram|Alpha
References
Chen, B. and Huang, J. "Deep Holes of Full-Length Reed-Solomon Codes." 21 Oct 2026. https://arxiv.org/abs/2610.29429.Hirschfeld, J. W. P. Projective Geometries over Finite Fields, 2nd ed. Oxford, England: Clarendon Press, 1998. https://doi.org/10.1093/oso/9780198502951.001.0001.Cite this as:
Weisstein, Eric W. "Hyperoval." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Hyperoval.html