Skip to main content
SpringerLink
Log in

Asymptotic existence of frame-GBTDs

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

Generalized balanced tournament designs (GBTDs) are an equivalent characterization of a class of equitable symbol weight codes. Motivated by the construction of GBTDs, we establish in this paper an asymptotic existence theorem for frame-GBTDs of type g n and block size k via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.

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. Chang K I. An existence theory for group divisible designs. PhD Thesis. Ohio: The Ohio State University, 1976

    Google Scholar 

  2. Chee Y M, Kiah H M, Ling A C H, et al. Optimal equitable symbol weight codes for power line communications. Cambridge, MA: Proceedings of the 2012 IEEE International Symposium on Information Theory, 2012, 671–675

    Google Scholar 

  3. Chee Y M, Kiah H M, Purkayastha P, et al. Importance of symbol equity in coded modulation for power line communications. IEEE Trans Commun, 2013, 61: 4381–4390

    Article  Google Scholar 

  4. Colbourn C J, Dinitz J H. The CRC Handbook of Combinatorial Designs. Boca Raton: CRC Press, 2007

    Google Scholar 

  5. Furino S C, Miao Y, Yin J X. Frames and Resolvable Designs. Boca Raton: CRC Press, 1996

    Google Scholar 

  6. Lamken E R, Wilson R M. Decompositions of edge-colored complete graphs. J Combin Theory Ser B, 2000, 89: 149–200

    Article  MathSciNet  Google Scholar 

  7. Liu J Q. Asymptotic existence theorems for frames and group divisible designs. J Combin Theory Ser A, 2007, 114: 410–420

    Article  MathSciNet  Google Scholar 

  8. Mohacsy H, Ray-Chaudhuri D R. An existence theorem for group divisible designs of large order. J Combin Theory Ser A, 2002, 98: 163–174

    Article  MathSciNet  Google Scholar 

  9. Schrijver A. Theory of Linear and Integer Programming. Chichester: John Wiley & Sons, 1986

    Google Scholar 

  10. Stinson D R. Combinatorial Designs: Construction and Analysis. New York: Springer-Verlag, 2004

    Google Scholar 

  11. Yan J, Yin J X. Constructions of optimal GDRP(n, λ; v)’s of type λ 1µm−1. Discrete Appl Math, 2008, 156: 2666–2678

    Article  MathSciNet  Google Scholar 

  12. Yan J, Yin J X, Wang C M. Generalized balanced tournament designs of block size 4. Des Codes Cryptogr, 2008, 46: 211–230

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215006, China

    Ling Jiang, Kun Wang & JianXing Yin

Authors
  1. Ling Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. JianXing Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to JianXing Yin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, L., Wang, K. & Yin, J. Asymptotic existence of frame-GBTDs. Sci. China Math. 58, 1795–1802 (2015). https://doi.org/10.1007/s11425-014-4907-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-014-4907-y

Keywords

MSC(2010)

Search

Navigation