Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

Regular pseudo-hyperovals and regular pseudo-ovals in even characteristic

Joseph A. Thas

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S. Rottey and G. Van de Voorde characterized regular pseudo-ovals of PG(3n1,q), q=2h, h>1 and n prime. Here an alternative proof is given and slightly stronger results are obtained.

Article information

Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 2 (2019), 77-84.

Received: 11 December 2017
Accepted: 14 January 2019
First available in Project Euclid: 5 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05B25: Finite geometries [See also 51D20, 51Exx] 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx] 51E21: Blocking sets, ovals, k-arcs 51E23: Spreads and packing problems

pseudo-hyperovals pseudo-ovals generalized arcs


Thas, Joseph A. Regular pseudo-hyperovals and regular pseudo-ovals in even characteristic. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 2, 77--84. doi:10.2140/iig.2019.17.77.

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  • W. Burau, Mehrdimensionale projektive und höhere Geometrie, Mathematische Monographien 5, VEB Deutscher Verlag der Wissenschaften, Berlin, 1961.
  • L. R. A. Casse, J. A. Thas, and P. R. Wild, “$(q^n+1)$-sets of ${\rm PG}(3n-1,q)$, generalized quadrangles and Laguerre planes”, Simon Stevin 59:1 (1985), 21–42.
  • J. W. P. Hirschfeld, Projective geometries over finite fields, 2nd ed., Oxford University, 1998.
  • J. W. P. Hirschfeld and J. A. Thas, General Galois geometries, 2nd ed., Springer, 2016.
  • W. M. Kantor, “Dimension and embedding theorems for geometric lattices”, J. Combin. Theory Ser. A 17 (1974), 173–195.
  • S. E. Payne and J. A. Thas, Finite generalized quadrangles, 2nd ed., European Mathematical Society, Zürich, 2009.
  • T. Penttila and G. Van de Voorde, “Extending pseudo-arcs in odd characteristic”, Finite Fields Appl. 22 (2013), 101–113.
  • S. Rottey and G. Van de Voorde, “Pseudo-ovals in even characteristic and ovoidal Laguerre planes”, J. Combin. Theory Ser. A 129 (2015), 105–121.
  • B. Segre, “Sulle ovali nei piani lineari finiti”, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. $(8)$ 17 (1954), 141–142.
  • J. A. Thas, “The $m$-dimensional projective space $S\sb{m}(M\sb{n}({\rm GF}(q)))$ over the total matrix algebra $M\sb{n}({\rm GF}(q))$ of the $n\times n$-matrices with elements in the Galois field ${\rm GF}(q)$”, Rend. Mat. $(6)$ 4 (1971), 459–532.
  • J. A. Thas, “Generalized ovals in ${\rm PG}(3n-1,q)$, with $q$ odd”, Pure Appl. Math. Q. 7:3, Special Issue: In honor of Jacques Tits (2011), 1007–1035.
  • J. A. Thas, K. Thas, and H. Van Maldeghem, Translation generalized quadrangles, Series in Pure Mathematics 26, World Scientific, Hackensack, NJ, 2006.