Skip to main content
Springer Nature Link
Log in

A new binary (17,4,5) constant weight code

  • Published:
Cryptography and Communications Aims and scope Submit manuscript

A Correction to this article was published on 01 March 2023

This article has been updated

Abstract

We describe a binary (17,4,5) constant weight code with 444 codewords, thus improving the lower bound for A(17,4,5) from 441 to 444. The code was discovered by a computer search implementing a new stochastic local search algorithm for the maximum independent set problem. The algorithm suggested is based on Generic Scuba Search, which is a known hybrid local search method exploiting neutrality in search landscapes.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Algorithm 2
Fig. 1

Similar content being viewed by others

Data availability

The datasets generated and analyzed during the current study and the source code used to produce them are available from the author on reasonable request.

Change history

References

  1. Brouwer, A.E.: Bounds for binary constant weight codes. website at https://www.win.tue.nl/~aeb/codes/Andw.html. Accessed 24 Nov 2020

  2. Tonchev, V.D.: Maximum disjoint bases and constant-weight codes. IEEE Trans. Inf. Theory 44(1), 333–334 (1998). https://doi.org/10.1109/18.651061

    Article  MathSciNet  MATH  Google Scholar 

  3. Ostergard, P.R.J.: Classification of binary constant weight codes. IEEE Trans. Inf. Theory 56(8), 3779–3785 (2010). https://doi.org/10.1109/TIT.2010.2050922

    Article  MathSciNet  MATH  Google Scholar 

  4. Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Elsevier, New York (2004)

    MATH  Google Scholar 

  5. Verel, S., Collard, P., Clergue, M.: Scuba search: when selection meets innovation. In: Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753), vol. 1. pp. 924–931 (2004)

  6. Marmion, M.E., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S.: NILS: A neutrality-based iterated local search and its application to flowshop scheduling. In: Merz, P., Hao, J.K. (eds.) Evolutionary Computation in Combinatorial Optimization, pp. 191–202. Springer, Berlin (2011)

    Chapter  Google Scholar 

  7. Marmion, M.E., Blot, A., Jourdan, L., Dhaenens, C.: Neutrality in the graph coloring problem. In: Nicosia, G., Pardalos, P. (eds.) Learning and Intelligent Optimization, pp. 125–130. Springer, Berlin (2013)

    Chapter  Google Scholar 

  8. Barnett, L.: Netcrawling-optimal evolutionary search with neutral networks. In: Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546). vol. 1, pp. 30–37. (2001)

  9. Marmion, M.E., Dhaenens, C., Jourdan, L., Liefooghe, A., Verel, S.: The Road to VEGAS: Guiding the search over neutral networks. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. GECCO ’11. New York, NY, USA: Association for Computing Machinery, pp. 1979–1986. Available from: https://doi.org/10.1145/2001576.2001842 (2011)

  10. Wu, Q., Hao, J.K.: A review on algorithms for maximum clique problems. Eur. J. Oper. Res. 242(3), 693–709 (2015). https://doi.org/10.1016/j.ejor.2014.09.064

    Article  MathSciNet  MATH  Google Scholar 

  11. Karp, R.M.: In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Reducibility among Combinatorial Problems. Boston, MA: Springer US. pp. 85–103. Available from: https://doi.org/10.1007/978-1-4684-2001-2_9 (1972)

  12. Friden, C., Hertz, A., de Werra, D.: Stabulus: a technique for finding stable sets in large graphs with tabu search. Computing 42(1), 35–44 (1989)

    Article  MATH  Google Scholar 

  13. Vitter, J.S.: Random sampling with a reservoir. ACM Trans. Math. Softw. 11(1), 37–57 (1985). https://doi.org/10.1145/3147.3165

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We would like to thank the anonymous reviewer for detailed comments and in particular, for the suggestion of the second search that led to a more structured code. We also would like to thank Prof. Jin-Kao Hao for providing advice on an earlier version of the manuscript.

Funding

The author did not receive support from any organization for the submitted work.

Author information

Authors and Affiliations

  1. Sarasota, Florida, United States

    Moshe Milshtein

Authors
  1. Moshe Milshtein
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

As a single author, the author confirms sole responsibility for all aspects of the research.

Corresponding author

Correspondence to Moshe Milshtein.

Ethics declarations

Ethical approval and consent to participate

Not applicable

Consent for publication

Not applicable

Competing interests

The author has no relevant financial or non-financial interests to disclose.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Milshtein, M. A new binary (17,4,5) constant weight code. Cryptogr. Commun. 15, 443–453 (2023). https://doi.org/10.1007/s12095-022-00611-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12095-022-00611-5

Keywords

Mathematics subject classification (2010)