Abstract
Let \({\mathcal {H}}\) be a non-empty set of hyperplanes in \(\text {PG}(4,q)\), q even, such that every point of \(\text {PG}(4,q)\) lies in either 0, \(\frac{1}{2}q^3\) or \(\frac{1}{2}(q^3+q^2)\) hyperplanes of \({\mathcal {H}}\), and every plane of \(\text {PG}(4,q)\) lies in 0 or at least \(\frac{1}{2}q\) hyperplanes of \({\mathcal {H}}\). Then \({\mathcal {H}}\) is the set of all hyperplanes which meet a given non-singular quadric Q(4, q) in a hyperbolic quadric.
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Acknowledgements
We would like the anonymous referee for their valuable feedback which improved both the content and exposition of this paper. A.M.W. Hui is supported by the Young Scientists Fund (Grant No. 11701035) of the National Natural Science Foundation of China, and J. Schillewaert by a University of Auckland FRDF Grant.
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Barwick, S.G., Hui, A.M.W., Jackson, WA. et al. Characterising hyperbolic hyperplanes of a non-singular quadric in \(\text {PG}(4,q)\). Des. Codes Cryptogr. 88, 33–39 (2020). https://doi.org/10.1007/s10623-019-00669-y
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DOI: https://doi.org/10.1007/s10623-019-00669-y