Modified generalized Hadamard matrices and constructions for transversal designs | Designs, Codes and Cryptography Skip to main content
Springer Nature Link
Log in

Modified generalized Hadamard matrices and constructions for transversal designs

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

Abstract

It is well known that there exists a transversal design TDλ[k; u] admitting a class regular automorphism group U if and only if there exists a generalized Hadamard matrix GH(u, λ) over U. Note that in this case the resulting transversal design is symmetric by Jungnickel’s result. In this article we define a modified generalized Hadamard matrix and show that transversal designs which are not necessarily symmetric can be constructed from these under a modified condition similar to class regularity even if it admits no class regular automorphism group.

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. Akiyama K., Ogawa M., Suetake C.: On STD6[18;3]’s and STD7[21;3]’s admitting a semiregular automorphism group of order 9, preprint.

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

  3. Davis J.A.: A note on products of relative difference sets. Des. Codes Cryptogr. 1, 117–119 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Drake D.A.: Partial λ-geometries and generalized Hadamard matrices over groups. Canad. J. Math. 31, 617–627 (1979)

    MathSciNet  Google Scholar 

  5. Hiramine Y.: On non-symmetric relative difference sets. Hokkaido Math. J. 37, 427–435 (2008)

    MATH  MathSciNet  Google Scholar 

  6. Hughes D.R., Piper F.C.: Projective Planes. Springer-Verlag, New York/Heidelberg/Berlin (1973)

    MATH  Google Scholar 

  7. Jungnickel D.: On automorphism groups of divisible designs. Canad. J. Math. 34, 257–297 (1982)

    MATH  MathSciNet  Google Scholar 

  8. Lüneburg H.: Translation Planes. Springer-Verlag, New York/Heidelberg/Berlin (1973)

    Google Scholar 

  9. Pott A.: Finite Geometry and Character Theory. Springer-Verlag, New York/Heidelberg/Berlin (1995)

    MATH  Google Scholar 

  10. Mavron V.C., Tonchev V.D.: On symmetric nets and generalized Hadamard matrices from affine designs. J. Geometry 67, 180–187 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Kumamoto University, Kurokami, Kumamoto, Japan

    Yutaka Hiramine

Authors
  1. Yutaka Hiramine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yutaka Hiramine.

Additional information

Communicated by Dieter Jungnickel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hiramine, Y. Modified generalized Hadamard matrices and constructions for transversal designs. Des. Codes Cryptogr. 56, 21–33 (2010). https://doi.org/10.1007/s10623-009-9337-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-009-9337-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation