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 Probl. Peredachi Inf., 2003, Volume 39, Issue 4, Pages 3–9 (Mi ppi311)

Information Theory and Coding Theory

Asymptotic Upper Bound for the Rate of $(w,r)$ Cover-Free Codes

V. S. Lebedev

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: A binary code is called a $(w,r)$ cover-free code if it is the incidence matrix of a family of sets where the intersection of any $w$ of the sets is not covered by the union of any other $r$ sets. Such a family is called a $(w,r)$ cover-free family. We obtain a new recurrent inequality for the rate of $(w,r)$ cover-free codes, which improves previously known upper bounds on the rate.

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English version:
Problems of Information Transmission, 2003, 39:4, 317–323

Bibliographic databases:

UDC: 621.391.15
Revised: 07.02.2003

Citation: V. S. Lebedev, “Asymptotic Upper Bound for the Rate of $(w,r)$ Cover-Free Codes”, Probl. Peredachi Inf., 39:4 (2003), 3–9; Problems Inform. Transmission, 39:4 (2003), 317–323

Citation in format AMSBIB
\Bibitem{Leb03} \by V.~S.~Lebedev \paper Asymptotic Upper Bound for the Rate of $(w,r)$ Cover-Free Codes \jour Probl. Peredachi Inf. \yr 2003 \vol 39 \issue 4 \pages 3--9 \mathnet{http://mi.mathnet.ru/ppi311} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2102715} \zmath{https://zbmath.org/?q=an:1096.94534} \transl \jour Problems Inform. Transmission \yr 2003 \vol 39 \issue 4 \pages 317--323 \crossref{https://doi.org/10.1023/B:PRIT.0000011270.09033.8f} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. H. K. Kim, V. S. Lebedev, “On the Optimality of Trivial $(w,r)$ Cover-Free Codes”, Problems Inform. Transmission, 40:3 (2004), 195–201
2. V. S. Lebedev, “Remark on the Uniqueness of $(w,r)$-Cover-Pree Codes”, Problems Inform. Transmission, 41:3 (2005), 199–203
3. V. S. Lebedev, “Asymptotic Bounds for the Rate of Colored Superimposed Codes”, Problems Inform. Transmission, 44:1 (2008), 112–118
4. V. S. Lebedev, “Separating codes and a new combinatorial search model”, Problems Inform. Transmission, 46:1 (2010), 1–6
5. Ahlswede R., Deppe Ch., Lebedev V., “Bounds for Threshold and Majority Group Testing”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011, 69–73
6. Hajiabolhassan H. Moazami F., “Some New Bounds for Cover-Free Families Through Biclique Covers”, Discrete Math., 312:24 (2012), 3626–3635
7. A. G. D'yachkov, I. V. Vorob'ev, N. A. Polyansky, V. Yu. Shchukin, “Bounds on the rate of disjunctive codes”, Problems Inform. Transmission, 50:1 (2014), 27–56
8. D'yachkov A.G. Vorobyev I.V. Polyanskii N.A. Shchukin V.Yu., “Bounds on the Rate of Superimposed Codes”, 2014 IEEE International Symposium on Information Theory (Isit), IEEE International Symposium on Information Theory, IEEE, 2014, 2341–2345
9. N. A. Polyansky, “Almost cover-free codes”, Problems Inform. Transmission, 52:2 (2016), 142–155
10. I. V. Vorob'ev, “Bounds on the rate of separating codes”, Problems Inform. Transmission, 53:1 (2017), 30–41
11. D'yachkov A.G. Vorobyev I.V. Polyanskii N.A. Shchukin V.Yu., “Cover-Free Codes and Separating System Codes”, Designs Codes Cryptogr., 82:1-2, SI (2017), 197–209
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