Skip to main content
SpringerLink
Log in

On the construction of (w, r) cover-free codes

  • Coding Theory
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

We construct a new class of concatenated cover-free codes. We prove that in this class there exists a sequence of (w, r) cover-free codes which has a nonzero limit rate for w, r = const. We consider application of cover-free codes to key distribution systems.

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

Similar content being viewed by others

References

  1. Kautz, W.H. and Singleton, R.C., Nonrandom Binary Superimposed Codes, IEEE Trans. Inform. Theory, 1964, vol. 10, no. 4, pp. 363–377.

    Article  MATH  Google Scholar 

  2. D’yachkov, A.G. and Rykov, V.V., Bounds on the Length of Disjunctive Codes, Probl. Peredachi Inf., 1982, vol. 18, no. 3, pp. 7–13 [Probl. Inf. Trans. (Engl. Transl.), 1982, vol. 18, no. 3, pp. 166–171].

    MATH  MathSciNet  Google Scholar 

  3. Erdős, P., Frankl, F., and Füredi, F., Families of Finite Sets in Which No Set Is Covered by the Union of r Others, Israel J. Math., 1985, vol. 51, no. 1–2, pp. 79–89.

    Article  MathSciNet  Google Scholar 

  4. Mitchell, C.J. and Piper, F.C., Key Storage in Secure Networks, Discrete Appl. Math., 1988, vol. 21, no. 3, pp. 215–228.

    Article  MATH  MathSciNet  Google Scholar 

  5. Stinson, D.R., On Some Methods for Unconditionally Secure Key Distribution and Broadcast Encryption, Des. Codes Cryptogr., 1997, vol. 12, no. 3, pp. 215–243.

    Article  MATH  MathSciNet  Google Scholar 

  6. Sagalovich, Yu.L., Separating Systems, Probl. Peredachi Inf., 1994, vol. 30, no. 2, pp. 14–35 [Probl. Inf. Trans. (Engl. Transl.), 1994, vol. 30, no. 2, pp. 105–123].

    MathSciNet  Google Scholar 

  7. Sagalovich, Yu.L., Completely Separating Systems, Probl. Peredachi Inf., 1982, vol. 18, no. 2, pp. 74–82 [Probl. Inf. Trans. (Engl. Transl.), 1982, vol. 18, no. 2, pp. 140–146].

    MathSciNet  Google Scholar 

  8. Kim, H.K. and Lebedev, V.S., On Optimal Superimposed Codes, J. Combin. Des., 2004, vol. 12, no. 2, pp. 79–91.

    Article  MATH  MathSciNet  Google Scholar 

  9. Vlǎduţ, S.G., Nogin, D.Yu., and Tsfasman, M.A., Algebrogeometricheskie kody. Osnovnye ponyatiya, Moscow: MCCME, 2003. Translated under the title Algebraic Geometry Codes. Basic Notions, Providence: Amer. Math. Soc., 2007.

    Google Scholar 

  10. Cohen, G.D. and Schaathun, H.G., Separating Codes: Constructions and Bounds, Proc. 6th Latin American Sympos. on Theoretical Informatics (LATIN 2004), Buenos Aires, Argentina, 2004, Farach-Colton, M., Ed., Lect. Notes Comp. Sci., vol. 2976, Berlin: Springer, 2004, pp. 322–328.

    Google Scholar 

Download references

Authors
  1. V. M. Sidelnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Yu. Prikhodov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.M. Sidelnikov, O.Yu. Prikhodov, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 1, pp. 36–40.

The Editorial Board thanks G.A. Kabatiansky for final preparation of the text.

Supported in part by the Russian Foundation for Basic Research, project nos. 05-01-01018 and 06-07-89170.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sidelnikov, V.M., Prikhodov, O.Y. On the construction of (w, r) cover-free codes. Probl Inf Transm 45, 32–36 (2009). https://doi.org/10.1134/S0032946009010049

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946009010049

Keywords

Search

Navigation