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arXiv · 1911.10798

Vandermonde sets and hyperovals

Kanat Abdukhalikov·Duy Ho
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Abstract

We consider relationships between Vandermonde sets and hyperovals. Hyperovals are Vandermonde sets, but, in general, Vandermonde sets are not hyperovals. We give necessary and sufficient conditions for a Vandermonde set to be a hyperoval. Therefore, we provide purely algebraic criteria for existence of hyperovals. Furthermore, we give necessary and sufficient conditions for the existence of hyperovals in terms of $g$-functions, which can be considered as an analog of Glynn's Theorem for o-polynomials.

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Kanat Abdukhalikov, Duy Ho. 2019-11-25. Vandermonde sets and hyperovals. https://doi.org/10.3934/amc.2021048

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