Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Note on the size of binary Armstrong codes

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

Abstract

We show for binary Armstrong codes Arm(2, k, n) that asymptotically n/k ≤ 1.224, while such a code is shown to exist whenever n/k ≤ 1.12. We also construct an Arm(2, n − 2, n) and Arm(2, n − 3, n) for all admissible n.

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

Similar content being viewed by others

References

  1. Katona G.O.H., Sali A., Schewe K.-D.: Codes that attain minimum distance in all possible directions. Cent. Eur. J. Math. 6, 1–11 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Keszler A.: Adatbázisok Extremális Kombinatorikai Problémái, Diploma thesis Budapest University of Technology and Economics (2008).

  3. Levenshtein V.I.: Universal bounds for codes and designs. In: Pless, V.S., Huffman, W.C. (eds) Handbook of Coding Theory, pp. 499–648. Elsevier, Amsterdam (1998)

    Google Scholar 

  4. McEliece R.J., Rodemich E.R., Rumsey H.C., Welch L.R.: New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities. IEEE Trans. Inf. Theory 23, 157–166 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  5. Östergård P.R.J., Pottonen O.: The perfect binary one-error-correcting codes of length 15: Part I—Classification. arXiv:0806.2513, Dec (2009).

  6. Sali A., Schewe K.-D.: Keys and Armstrong databases in trees with restructuring. Acta Cybernetica 18, 529–556 (2008)

    MATH  MathSciNet  Google Scholar 

  7. Sali A., Székely L.: On the existence of Armstrong instances with bounded domains. Lect. Notes Comp. Sci. 4932, 151–157 (2008)

    Article  Google Scholar 

  8. Sali A.: Coding theory motivated by relational databases. Lect. Notes Comp. Sci. 6834, 96–113 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Aart Blokhuis & Andries E. Brouwer

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364, Budapest, Hungary

    Attila Sali

  3. Department of Computer Science, Budapest University of Technology and Economics, Budapest, Hungary

    Attila Sali

Authors
  1. Aart Blokhuis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andries E. Brouwer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Attila Sali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Attila Sali.

Additional information

Communicated by V. A. Zinoviev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blokhuis, A., Brouwer, A.E. & Sali, A. Note on the size of binary Armstrong codes. Des. Codes Cryptogr. 71, 1–4 (2014). https://doi.org/10.1007/s10623-012-9711-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-012-9711-5

Keywords

Mathematics Subject Classification

Search

Navigation