Designs, Codes and Cryptography

, Volume 82, Issue 1–2, pp 197–209 | Cite as

Cover-free codes and separating system codes

  • A. G. D’yachkovEmail author
  • I. V. VorobyevEmail author
  • N. A. Polyanskii
  • V. Yu. Shchukin


We give some relations between the asymptotic rates of cover-free (CF) codes, separating system (SS) codes and completely separating system (CSS) codes. We also provide new upper bounds on the asymptotic rate of SS codes based on known results for CF and CSS codes. Finally, we derive a random coding bound for the asymptotic rate of SS codes and give tables of numerical values corresponding to our improved upper bounds.


Separating system codes Cover-free codes Completely separating system codes Frameproof codes Digital fingerprinting 

Mathematics Subject Classification

94B25 94B65 



I.V. Vorobyev, N.A. Polyanskii and V.Yu. Shchukin have been supported in part by the Russian Science Foundation under Grant No. 14-50-00150.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussian Federation
  2. 2.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussian Federation

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