Skip to main content
Log in

Divisible designs with dual translation group

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

Abstract

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. André J (1954) Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe. Math Z 60:156–186

    Article  MATH  MathSciNet  Google Scholar 

  2. Blunck A, Havlicek H, Zanella C (2007) Lifting of divisible designs. Designs, Codes and Cryptography 42:1–14

    Article  MathSciNet  Google Scholar 

  3. Cerroni C, Schulz R-H (2000) Divisible designs admitting GL(3, q) as an automorphism group. Geom Dedicata 83:343–350

    Article  MATH  MathSciNet  Google Scholar 

  4. Cerroni C, Schulz R-H (2001) Divisible designs admitting, as an automorphism group, an orthogonal group or a unitary group. In: Jungnickel D. et al (eds) Finite fields and applications, Springer, Verlag, Berlin, pp. 95–108. Proc. 5th internat. conf. on finite fields and applications

  5. Cerroni C, Spera AG (1999) On divisible designs and twisted field planes. J Comb Des 7:453–464

    Article  MATH  MathSciNet  Google Scholar 

  6. Giese S (2005) Block-zerlegbare divisible Designs. URL: http://www.diss.fu-berlin.de/2005/347, Dissertation

  7. Giese S (2006) Block-decomposability of divisible designs. Submitted to J Comb Des

  8. Giese S (2006) Constructing block-decomposable divisible designs. Preprint

  9. Giese S, Havlicek H, Schulz R-H (2005) Some constructions of divisible designs from Laguerre geometries. Discrete Math 301:74–82

    Article  MATH  MathSciNet  Google Scholar 

  10. Lüneburg H (1980) Translation planes. Springer, New York

    MATH  Google Scholar 

  11. Schulz R-H (1985) On the classification of translation group-divisible designs. Euro. J. Comb 6:369–374

    MATH  MathSciNet  Google Scholar 

  12. Schulz R-H (1987) On translation transversal designs with λ > 1. Arch. Math 49:97–102

    Article  MATH  MathSciNet  Google Scholar 

  13. Schulz R-H, Spera AG (1998) Construction of divisible designs from translation planes. Eur. J. Comb 19(4):479–486

    Article  MATH  MathSciNet  Google Scholar 

  14. Schulz R-H, Spera AG (1998) Divisible designs admitting a Suzuki group as an automorphism group. Boll. Unione Mat Ital 8(1B):705–714

    MathSciNet  Google Scholar 

  15. Spera AG (1992) t-Divisible designs from imprimitive permutation groups. Eur. J. Comb 13:409–417

    Article  MATH  MathSciNet  Google Scholar 

  16. Spera AG (2000) Divisible designs associated with translation planes admitting a 2-transitive collineation group on the points at infinity. Aequationes Math 59(1–2):191–200

    Article  MATH  MathSciNet  Google Scholar 

  17. Stroppel M (1992) Reconstruction of incidence geometries from groups of automorphisms. Arch. Math 58:621–624

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sabine Giese.

Additional information

Communicated by A. Pott.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Giese, S., Schulz, RH. Divisible designs with dual translation group. Des Codes Crypt 43, 41–45 (2007). https://doi.org/10.1007/s10623-007-9056-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-007-9056-7

Keywords

AMS Classification

Navigation