Uniqueness of some cyclic projective planes | Designs, Codes and Cryptography
Skip to main content
Springer Nature Link
Log in

Uniqueness of some cyclic projective planes

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

Abstract

For n < 41 and for \({{n \in }}\) {121, 125, 128, 169, 256, 1024}, every cyclic projective plane of order n is desarguesian.

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. Baumert L.D., Gordon D.M.: On the existence of cyclic difference sets with small parameters. In: High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams. Fields Inst. Commun. 41, 61–68 (2004)

    MathSciNet  Google Scholar 

  2. Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge University Press (1999).

  3. Bruck R.H.: Quadratic extensions of cyclic planes. Proc. Symp. Appl. Math. 10, 15–44 (1960)

    MathSciNet  Google Scholar 

  4. Gordon D.M.: The prime power conjecture is true for n < 2,000,000. J. Comb. 1, 101–107 (1994)

    Google Scholar 

  5. Gordon B., Mills W.H., Welch L.R.: Some new difference sets. Can. J. Math. 14, 614–625 (1962)

    MATH  MathSciNet  Google Scholar 

  6. Hall M.: Cyclic projective planes. Duke Math. J. 14, 1079–1090 (1947)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hall M.: A survey of difference sets. Proc. Am. Math. Soc. 7, 975–986 (1957)

    Article  MATH  Google Scholar 

  8. Jungnickel D.: The isomorphism problem for Abelian projective planes. Appl. Algebra Eng. Commun. Comput. 19, 195–200 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. McFarland R.L., Rice B.F.: Translates and multipliers of abelian difference sets. Proc. Am. Math. Soc. 68, 375–379 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  10. Singer J.: A theorem in finite projective geometry and some applications to number theory. Trans. Am. Math. Soc. 43, 377–385 (1938)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Yiwei Huang & Bernhard Schmidt

Authors
  1. Yiwei Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernhard Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bernhard Schmidt.

Additional information

Communicated by D.Jungnickel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, Y., Schmidt, B. Uniqueness of some cyclic projective planes. Des. Codes Cryptogr. 50, 253–266 (2009). https://doi.org/10.1007/s10623-008-9229-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-008-9229-z

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation