Skip to main content
SpringerLink
Log in

Upper bounds for parent-identifying set systems

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

Abstract

We derive new upper bounds on the size set families having the c-identifiable parent property (c-IPP) and the c-traceability property (c-TA) and compare these bounds to similar results on parent-identifying codes.

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.

Similar content being viewed by others

References

  1. Alon N., Stav U.: New bounds on parent-identifying codes: the case of multiple parents. Comb. Probab. Comput. 13(6), 795–807 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blackburn S.R.: An upper bound on the size of a code with the k-identifiable parent property. J. Comb. Theory, Ser. A 102(1), 179–185 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chor B., Fiat A., Naor M., Pinkas B.: Tracing traitors. IEEE Trans. Inform. Theory 46(3), 893–910 (2000)

    Article  MATH  Google Scholar 

  4. Collins M.J.: Upper bounds for set systems with the identifiable parent property. In: Safavi-Naini R. (ed.) ICITS, vol. 5155 of Lecture Notes in Computer Science, pp. 100–106. Springer (2008).

  5. Fernandez M., Navau J.C., Soriano M., Domingo N.: A note about the traceability properties of linear codes. In: Nam K.-H., Rhee G. (eds.) ICISC, vol. 4817 of Lecture Notes in Computer Science, pp. 251–258. Springer (2007).

  6. Füredi Z., Erdős P., Frankl P.: Families of finite sets in which no set is covered by the union of r others. Israel J. Math. 51(1), 79–89 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  7. Staddon J., Stinson D.R., Wei R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inform. Theory 47(3), 1042–1049 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Stinson D.R., Wei R.: Combinatorial properties and constructions of traceability schemes and frameproof codes. SIAM J. Discrete Math. 11, 41–53 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Michael J. Collins

Authors
  1. Michael J. Collins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael J. Collins.

Additional information

Communicated by H. Wang.

An earlier version of this paper appeared in [4]. Sandia National Laboratories—This is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Collins, M.J. Upper bounds for parent-identifying set systems. Des. Codes Cryptogr. 51, 167–173 (2009). https://doi.org/10.1007/s10623-008-9253-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-008-9253-z

Keywords

Mathematics Subject Classification (2000)

Search

Navigation