Glasnik Matematicki, Vol. 58, No. 2 (2023), 327-330. \( \)

SPLITNESS OF THE VERONESEAN DUAL HYPEROVALS: A QUICK PROOF

Ulrich Dempwolff

Department of Mathematics, Technical University Kaiserslautern, 67653 Kaiserslautern, Germany
e-mail:dempwolff@mathematik.uni-kl.de

Abstract.   Satoshi Yoshiara shows in [7] that the Veronesean dual hyperovals over \({\mathbb F}_2\) are of split type. So far there exists no published proof that a Veronesean dual hyperoval over any finite field of even characteristic is of split type. In this note we give a quick proof of this fact.

2020 Mathematics Subject Classification.   51A45, 05B25

Key words and phrases.   Dimensional dimensional dual hyperoval

https://doi.org/10.3336/gm.58.2.12

References:

1. U. Dempwolff and Y. Edel, The radical of binary dimensional dual hyperovals, Finite Fields Appl. 91 (2023), paper no. 102257.
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2. U. Dempwolff and Y. Edel, The webpage associated with [1].
   Link

3. H. Taniguchi, On a family of dual hyperovals over \({\rm GF}(q)\) with \(q\) even, European J. Combin. 26 (2005), 195–199.
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5. S. Yoshiara, Dimensional dual arcs–a survey, in Finite geometries, groups and computation, Walter de Gruyter GmbH & Co. KG, Berlin, 2006, pp. 247–266.
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6. S. Yoshiara, Notes on Taniguchi's dimensional dual hyperovals, European J. Combin. 28 (2007), 674–684.
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7. S. Yoshiara, Splitness of the Veronesean and the Taniguchi dual hyperovals, Discrete Math. 342 (2019), 844–854.
   MathSciNet    CrossRef