Skip to main content
SpringerLink
Log in

The Independence Number of the Orthogonality Graph in Dimension 2k

  • Published:
Combinatorica Aims and scope Submit manuscript

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

References

  1. C. Bachoc, D. C. Gijswijt, A. Schrijver and F. Vallentin: Invariant semidef-inite programs, in: Handbook on semidefinite, conic and polynomial optimization (M. F. Anjos and J. B. Lasserre, eds.), Springer, New York, 2012, 219–269.

    Google Scholar 

  2. G. Brassard, R. Cleve and A. Tapp: Cost of exactly simulating quantum entanglement with classical communication, Phys. Rev. Lett. 83 (1999), 1874–1877.

    Article  Google Scholar 

  3. H. Buhrman, R. Cleve and A. Widgerson: Quantum vs. classical communication and computation, in: Proceedings of the 30th Annual ACM Symposium on the Theory of Computing, Dallas, TX, USA, 1998, 63–68.

    Google Scholar 

  4. P. J. Cameron: Problems from CGCS Luminy, May 2007, European J. Combin. 31 (2010), 644–648.

    Article  MathSciNet  Google Scholar 

  5. P. Delsarte: An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl., No. 10, 1973.

  6. N. J. Fine: Binomial coefficients modulo a prime, Amer. Math. Monthly 54 (1947), 589–592.

    Article  MathSciNet  Google Scholar 

  7. P. Frankl: Orthogonal vectors in the n-dimensional cube and codes with missing distances, Combinatorica 6 (1986), 279–285.

    Article  MathSciNet  Google Scholar 

  8. P. Frankl and V. Rödl: Forbidden intersections, Trans. Amer. Math. Soc. 300 (1987), 259–286.

    Article  MathSciNet  Google Scholar 

  9. V. Galliard: Classical pseudo-telepathy and colouring graphs, diploma thesis, ETH Zurich, 2001; available at https://doi.org/math.galliard.ch/Cryptography/Papers/PseudoTelepathy/SimulationOfEntanglement.pdf.

    Google Scholar 

  10. V. Galliard, A. Tapp and S. Wolf: The impossibility of pseudo-telepathy without quantum entanglement, in: Proceedings 2003 IEEE International Symposium on Information Theory, Yokohama, Japan, 2003.

    Google Scholar 

  11. D. C. Gijswijt, H. D. Mittelmann and A. Schrijver: Semidefinite code bounds based on quadruple distances, IEEE Trans. Inform. Theory 58 (2012), 2697–2705.

    Article  MathSciNet  Google Scholar 

  12. C. D. Godsil and M. W. Newman: Coloring an orthogonality graph, SIAM J. Discrete Math. 22 (2008), 683–692.

    Article  MathSciNet  Google Scholar 

  13. E. de Klerk and D. V. Pasechnik: A note on the stability number of an orthogonality graph, European J. Combin. 28 (2007), 1971–1979.

    Article  MathSciNet  Google Scholar 

  14. M. Laurent: Strengthened semidefinite programming bounds for codes, Math. Program. 109 (2007), 239–261.

    Article  MathSciNet  Google Scholar 

  15. M. W. Newman: Independent sets and eigenspaces, thesis, University of Waterloo, 2004.

    Google Scholar 

  16. A. Schrijver: New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory 51 (2005), 2859–2866.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

We thank the anonymous referee for solving the case n=24.

Author information

Authors and Affiliations

  1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Ferdinand Ihringer

  2. Research Center for Pure and Applied Mathematics Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Hajime Tanaka

Authors
  1. Ferdinand Ihringer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hajime Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Ferdinand Ihringer or Hajime Tanaka.

Additional information

The first author is supported by a postdoctoral fellowship of the Research Foundation - Flanders (FWO)

The second author is supported by JSPS KAKENHI Grant Number JP17K05156.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ihringer, F., Tanaka, H. The Independence Number of the Orthogonality Graph in Dimension 2k. Combinatorica 39, 1425–1428 (2019). https://doi.org/10.1007/s00493-019-4134-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00493-019-4134-9

Search

Navigation