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Codes Identifying Sets of Vertices

  • Tero Laihonen
  • Sanna Ranto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2227)

Abstract

We consider identifying and strongly identifying codes. Finding faulty processors in a multiprocessor system gives the motivation for these codes. Constructions and lower bounds on these codes are given.We provide two infinite families of optimal (1,<= 2)-identifying codes, which can find malfunctioning processors in a binary hypercube F2 n

Also two infinite families of optimal codes are given in the corresponding case of strong identification. Some results on more general graphs are as well provided.

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References

  1. 1.
    U. Blass, I. Honkala, S. Litsyn: Bounds on identifying codes. Discrete Math., to appearGoogle Scholar
  2. 2.
    U. Blass, I. Honkala, S. Litsyn: On binary codes for identification. J. Combin. Des., 8 (2000) 151–156zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    I. Charon, I. Honkala, O. Hudry, A. Lobstein: General bounds for identifying codes in some infinite regular graphs. Electronic Journal of Combinatorics, submittedGoogle Scholar
  4. 4.
    G. Cohen, I. Honkala, S. Litsyn, A. Lobstein: Covering Codes. Elsevier, Amsterdam, the Netherlands (1997)zbMATHGoogle Scholar
  5. 5.
    G. Cohen, I. Honkala, A. Lobstein, G. Zémor: On identifying codes. In: Barg, A., Litsyn, S. (eds.): Codes and Association Schemes. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 56 (2001) 97–109Google Scholar
  6. 6.
    G. Exoo: Computational results on identifying t-codes. preprintGoogle Scholar
  7. 7.
    I. Honkala: On the identifying radius of codes. Proceedings of the Seventh Nordic Combinatorial Conference, Turku, (1999) 39–43Google Scholar
  8. 8.
    I. Honkala: Triple systems for identifying quadruples. Australasian J. Combinatorics, to appearGoogle Scholar
  9. 9.
    I. Honkala, T. Laihonen, S. Ranto: On codes identifying sets of vertices in Hamming spaces. Des. Codes Cryptogr., to appearGoogle Scholar
  10. 10.
    I. Honkala, T. Laihonen, S. Ranto: On strongly identifying codes. Discrete Math., to appearGoogle Scholar
  11. 11.
    I. Honkala, T. Laihonen, S. Ranto: Codes for strong identification. Electronic Notes in Discrete Mathematics, to appearGoogle Scholar
  12. 12.
    M.G. Karpovsky, K. Chakrabarty, L. B. Levitin, On a new class of codes for identifying vertices in graphs. IEEE Trans. Inform. Theory, 44 (1998) 599–611zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    T. Laihonen: Sequences of optimal identifying codes. IEEE Trans. Inform. Theory, submittedGoogle Scholar
  14. 14.
    T. Laihonen: Optimal codes for strong identification, European J. Combinatorics, submittedGoogle Scholar
  15. 15.
    T. Laihonen, S. Ranto: Families of optimal codes for strong identification. Discrete Appl. Math., to appearGoogle Scholar
  16. 16.
    S. Ranto, I. Honkala, T. Laihonen: Two families of optimal identifying codes in binary Hamming spaces. IEEE Trans. Inform. Theory, submittedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tero Laihonen
    • 1
  • Sanna Ranto
    • 2
  1. 1.Department of Mathematics and Turku Centre for Computer Science TUCSUniversity of TurkuTurkuFinland
  2. 2.Turku Centre for Computer Science TUCSUniversity of TurkuTurkuFinland

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