Some constructions on the Hermitian surface | Designs, Codes and Cryptography Skip to main content
Springer Nature Link
Log in

Some constructions on the Hermitian surface

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

In the geometric setting of commuting orthogonal and unitary polarities we construct an infinite family of complete (q + 1)2–spans of the Hermitian surface \({\mathcal {H}(3, q^2)}\) , q odd. A construction of an infinite family of minimal blocking sets of \({\mathcal {H}(3, q^2)}\) , q odd, admitting PSL 2(q), is also provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aguglia A., Cossidente A., Ebert G.L.: Complete spans on Hermitian varieties. Des. Codes Cryptogr. 29(1–3), 7–15 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aguglia A., Cossidente A., Ebert G.L.: On pairs of permutable Hermitian surface. Discrete Math. 301, 28–33 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bamberg J., Kelly S., Law M., Penttila T.: Tim, Tight sets and m-ovoids of finite polar spaces. J. Combin. Theory Ser. A 114(7), 1293–1314 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cossidente A., Ebert G.L.: Permutable polarities and a class of ovoids of the Hermitian surface. European J. Combin. 25, 1059–1066 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ebert G.L., Hirschfeld J.W.P.: Complete systems of lines on a Hermitian surface over a finite field. Des. Codes Cryptogr. 17(1–3), 253–268 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kleidman P.B., Liebeck M.: The Subgroup Structure of the Finite Classical Groups. LMS Lecture Note Series, vol. 129. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  7. Payne S.E., Thas J.A.: Finite Generalized Quadrangles, Research Notes in Mathematics, vol. 104. Pitman, Boston-London-Melbourne (1984).

  8. Segre B.: Forme e geometrie Hermitiane con particolare riguardo al caso finito. Ann. Mat. Pura Appl. 70, 1–201 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sved M.: Baer subspaces in the n-dimensional projective space. In: Combinatorial Mathematics, X (Adelaide, 1982), Lecture Notes in Mathematics, vol. 1036, pp. 375–391. Springer, Berlin (1983).

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematicae Informatica, Università della Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy

    Antonio Cossidente

Authors
  1. Antonio Cossidente
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Cossidente.

Additional information

Communicated by S. Ball.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cossidente, A. Some constructions on the Hermitian surface. Des. Codes Cryptogr. 51, 123–129 (2009). https://doi.org/10.1007/s10623-008-9248-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-008-9248-9

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation