Skip to main content
SpringerLink
Log in

Distorting symmetric designs

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

Abstract

A simple replacement approach is used to construct new symmetric and affine designs from projective or affine spaces. This is used to construct symmetric designs with a given automorphism group, to study GMW designs, and to construct new affine designs whose automorphism group fixes a point and has just two point- and block-orbits.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Babai L. (1974) On the minimum order of graphs with given group. Can. Math. Bull. 17: 467–470

    MATH  MathSciNet  Google Scholar 

  2. Beth T., Jungnickel D., Lenz H. (1999) Design Theory, vol. 1. Cambridge University Press, Cambridge

    Google Scholar 

  3. Dembowski P. (1968) Finite Geometries. Springer, Berlin

    MATH  Google Scholar 

  4. Dembowski P., Wagner A. (1960) Some characterizations of finite projective spaces. Arch. Math. 11: 465–469

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  6. Jackson W.-A. (1993) A characterization of Hadamard designs with SL(2, q) acting transitively. Geometriae Dedicate 46: 197–206

    Article  MATH  Google Scholar 

  7. Jackson W.-A., Wild P.R. (1997) On GMW designs and cyclic Hadamard designs. Des. Codes Cryptogr. 10: 185–191

    Article  MATH  MathSciNet  Google Scholar 

  8. Jungnickel D. (1984) The number of designs with classical parameters grows exponentially. Geometriae Dedicate 16: 167–178

    MATH  MathSciNet  Google Scholar 

  9. Kantor W.M. (1994) Automorphisms and isomorphisms of symmetric and affine designs. J. Algebr. Comb. 3: 307–338

    Article  MATH  MathSciNet  Google Scholar 

  10. Kantor W.M. (2001) Note on GMW designs. Eur. J. Comb. 22: 63–69

    Article  MATH  MathSciNet  Google Scholar 

  11. Merchant E. (2006) Exponentially many Hadamard designs. Des. Codes Cryptogr. 38: 297–308

    Article  MathSciNet  Google Scholar 

  12. Pott A. (1995) Finite Geometry and Character Theory. Springer, Berlin

    MATH  Google Scholar 

  13. Shrikhande S.S. (1951) On the nonexistence of affine resolvable balanced incomplete block designs. Sankhyä 11: 185–186

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Kaiserslautern, Kaiserslautern, 6750, Germany

    Ulrich Dempwolff

  2. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    William M. Kantor

Authors
  1. Ulrich Dempwolff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William M. Kantor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William M. Kantor.

Additional information

Communicated by A. Pott.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dempwolff, U., Kantor, W.M. Distorting symmetric designs. Des. Codes Cryptogr. 48, 307–322 (2008). https://doi.org/10.1007/s10623-008-9209-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-008-9209-3

Keywords

AMS Classifications

Search

Navigation