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Designs, Codes and Cryptography

, Volume 77, Issue 2–3, pp 301–319 | Cite as

On tight bounds for binary frameproof codes

  • Chuan Guo
  • Douglas R. Stinson
  • Tran van Trung
Article

Abstract

In this paper, we study \(w\)-frameproof codes, which are equivalent to \(\{1,w\}\)-separating hash families. Our main results concern binary codes, which are defined over an alphabet of two symbols. For all \(w \ge 3\), and for \(w+1 \le N \le 3w\), we show that an \({\mathsf {SHF}}(N; n,2, \{1,w \})\) exists only if \(n \le N\), and an \({\mathsf {SHF}}(N; N,2, \{1,w \})\) must be a permutation matrix of degree \(N\).

Keywords

Code Frameproof code Hash family Separating hash family 

Mathematics Subject Classification

94A60 

Notes

Acknowledgments

D. Stinson’s research is supported by NSERC discovery Grant 203114-11.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chuan Guo
    • 1
  • Douglas R. Stinson
    • 1
  • Tran van Trung
    • 2
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Institut für Experimentelle MathematikUniversität Duisburg-EssenEssenGermany

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