Abstract
We show that a symmetric, doubly dual hyperoval has an odd rank. This is a weak support for the conjecture that doubly dual hyperovals over \(\mathbb{F }_2\) only exist, if the rank of the dual hyperoval is odd (see [2]).
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Notes
More common is notion \((n-1)\)-dimensional dual hyperoval for a dual hyperoval of rank \(n\) referring to the projective dimension of vectorspaces (see [5, Def. 2.1, 2.3]).
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We thank the reviewers for helpful comments and suggestions leading to a more transparent text.
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Communicated by T. Penttila.
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Dempwolff, U. Symmetric doubly dual hyperovals have an odd rank. Des. Codes Cryptogr. 74, 153–157 (2015). https://doi.org/10.1007/s10623-013-9847-y
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DOI: https://doi.org/10.1007/s10623-013-9847-y