Designs, Codes and Cryptography

, Volume 71, Issue 1, pp 1–4 | Cite as

Note on the size of binary Armstrong codes

  • Aart Blokhuis
  • Andries E. Brouwer
  • Attila SaliEmail author


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.


Coding theory Databases Armstrong codes 

Mathematics Subject Classification

94B60 94B65 


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  1. 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)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Keszler A.: Adatbázisok Extremális Kombinatorikai Problémái, Diploma thesis Budapest University of Technology and Economics (2008).Google Scholar
  3. 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. 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)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 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).Google Scholar
  6. 6.
    Sali A., Schewe K.-D.: Keys and Armstrong databases in trees with restructuring. Acta Cybernetica 18, 529–556 (2008)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Sali A., Székely L.: On the existence of Armstrong instances with bounded domains. Lect. Notes Comp. Sci. 4932, 151–157 (2008)CrossRefGoogle Scholar
  8. 8.
    Sali A.: Coding theory motivated by relational databases. Lect. Notes Comp. Sci. 6834, 96–113 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Aart Blokhuis
    • 1
  • Andries E. Brouwer
    • 1
  • Attila Sali
    • 2
    • 3
    Email author
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  3. 3.Department of Computer ScienceBudapest University of Technology and EconomicsBudapestHungary

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