English

Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric \Q(2n,q)

Combinatorics 2021-11-19 v1

Abstract

We provide a natural characterisation for the sets of elliptic and hyperbolic hyperplanes of the parabolic quadric Q(2n,q) when q is even. This characterisation is based on the number of elements of these sets through points and codimension 2 spaces and generalises [S. Barwick, A. Hui, and W-A. Jackson. Characterising elliptic solids of Q(4,q), q even. Discrete Math., 343 (6) (2020), 111857] and [S. Barwick, A. Hui, W-A. Jackson, and J. Schillewaert. Characterising hyperbolic solids of Q(4,q), q even. Des. Codes Cryptogr., 88 (1) (2020), 33--39.].

Keywords

Cite

@article{arxiv.2111.09443,
  title  = {Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric \Q(2n,q)},
  author = {Jeroen Schillewaert and Geertrui Van de Voorde},
  journal= {arXiv preprint arXiv:2111.09443},
  year   = {2021}
}

Comments

To appear in Finite Fields and their Applications