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A Characterization of the Finite Veronesean by Intersection Properties

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Abstract

A combinatorial characterization of the Veronese variety of all quadrics in PG(n, q) by means of its intersection properties with respect to subspaces is obtained. The result relies on a similar combinatorial result on the Veronesean of all conics in the plane PG(2, q) by Ferri [Atti Accad. Naz. Lincei Rend. 61(6), 603–610 (1976)], Hirschfeld and Thas [General Galois Geometries. Oxford University Press, New York (1991)], and Thas and Van Maldeghem [European J. Combin. 25(2), 275–285 (2004)], and a structural characterization of the quadric Veronesean by Thas and Van Maldeghem [Q. J. Math. 55(1), 99–113 (2004)].

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References

  1. Del Fra, A.: On d-dimensional dual hyperovals. Geom. Dedicata 79(2), 157–178 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ferri O.: Su di una caratterizzazione grafica della superficie di Veronese di un S 5,q . Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 61(6), 603–610 (1976)

    MathSciNet  Google Scholar 

  3. Hirschfeld J.W.P.: Finite Projective Spaces of Three Dimensions. Oxford University Press, New York (1985)

    MATH  Google Scholar 

  4. Hirschfeld J.W.P., Thas J.A.: General Galois Geometries. Oxford University Press, New York (1991)

    MATH  Google Scholar 

  5. Segre B.: Ovals in a finite projective plane. Canad. J. Math. 7, 414–416 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  6. Tallini, G.: Una proprietà grafica caratteristica della superficie di Veronese negli spazi finiti. I, II. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 24, 19–23, 135–138 (1958)

  7. Thas J.A., Van Maldeghem H.: On Ferri’s characterization of the finite quadric Veronesean J. Combin. Theory Ser. A 110(2), 217–221 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Thas J.A., Van Maldeghem H.: Characterizations of the finite quadric Veroneseans . Q. J. Math. 55(1), 99–113 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Thas J.A., Van Maldeghem H.: Classification of finite Veronesean caps. European J. Combin. 25(2), 275–285 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zanella C.: Linear sections of the finite Veronese varieties and authentication systems defined using geometry. Des. Codes Cryptogr. 13(2), 199–212 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, ULB, CP 216, Bd du Triomphe, 1050, Brussels, Belgium

    J. Schillewaert

  2. Department of Mathematics, Ghent University, Krijgslaan 281-S22, B-9000, Gent, Belgium

    J. A. Thas & H. Van Maldeghem

Authors
  1. J. Schillewaert
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  2. J. A. Thas
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  3. H. Van Maldeghem
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Correspondence to J. Schillewaert.

Additional information

The research of the first author took place within the project “Linear codes and cryptography” of the Fund for Scientific Research Flanders (FWO-Vlaanderen) (Project nr. G.0317.06), and is supported by the Interuniversitary Attraction Poles Programme-Belgian State-Belgian Science Policy: project P6/26-Bcrypt.

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Schillewaert, J., Thas, J.A. & Van Maldeghem, H. A Characterization of the Finite Veronesean by Intersection Properties. Ann. Comb. 16, 331–348 (2012). https://doi.org/10.1007/s00026-012-0136-7

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  • DOI: https://doi.org/10.1007/s00026-012-0136-7

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