VANDERMONDE SETS, HYPEROVALS AND NIHO BENT FUNCTIONS

Abdukhalikov K. Ho D.
October 2023 American Institute of Mathematical Sciences

Advances in Mathematics of Communications
2023 #17 Issue 5 1235 - 1250 pp.

We consider relationships between Vandermonde sets and hyper-ovals. 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 in terms of power sums. Therefore, we provide purely algebraic criteria for the 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. We also get some important applications to Niho bent functions.

hyperovals , Niho bent functions , Ovals , power sums , Vandermonde sets

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Institute of Mathematics and Mathematical Modeling

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