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Probl. Peredachi Inf., 1982, Volume 18, Issue 3, Pages 7–13 (Mi ppi1232)  

This article is cited in 32 scientific papers (total in 32 papers)

Information Theory and Coding Theory

Bounds on the Length of Disjunctive Codes

A. G. D'yachkov, V. V. Rykov


Abstract: A new lower bound for the length of disjunctive codes [W. H. Kautz and R. C. Singleton, IEEE Trans. Inf. Theory, 1964, vol. 10, no. 4, pp. 363–377] is proved. An upper bound obtained by the method of random coding is given.

Full text: PDF file (666 kB)

English version:
Problems of Information Transmission, 1982, 18:3, 166–171

Bibliographic databases:

UDC: 621.391.15
Received: 06.06.1981

Citation: A. G. D'yachkov, V. V. Rykov, “Bounds on the Length of Disjunctive Codes”, Probl. Peredachi Inf., 18:3 (1982), 7–13; Problems Inform. Transmission, 18:3 (1982), 166–171

Citation in format AMSBIB
\Bibitem{DyaRyk82}
\by A.~G.~D'yachkov, V.~V.~Rykov
\paper Bounds on the Length of Disjunctive Codes
\jour Probl. Peredachi Inf.
\yr 1982
\vol 18
\issue 3
\pages 7--13
\mathnet{http://mi.mathnet.ru/ppi1232}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=711896}
\zmath{https://zbmath.org/?q=an:0524.94015|0507.94013}
\transl
\jour Problems Inform. Transmission
\yr 1982
\vol 18
\issue 3
\pages 166--171


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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. V. S. Lebedev, “Asymptotic Upper Bound for the Rate of $(w,r)$ Cover-Free Codes”, Problems Inform. Transmission, 39:4 (2003), 317–323  mathnet  crossref  mathscinet  zmath
    2. H. K. Kim, V. S. Lebedev, “On the Optimality of Trivial $(w,r)$ Cover-Free Codes”, Problems Inform. Transmission, 40:3 (2004), 195–201  mathnet  crossref  mathscinet  zmath
    3. V. S. Lebedev, “Remark on the Uniqueness of $(w,r)$-Cover-Pree Codes”, Problems Inform. Transmission, 41:3 (2005), 199–203  mathnet  crossref  mathscinet  zmath
    4. S. Hong, Kim Hyun Kwang, S. N. Kapralov, Oh Dong Yeol, “Uniqueness of Some Optimal Superimposed Codes”, Problems Inform. Transmission, 43:2 (2007), 113–123  mathnet  crossref  mathscinet  isi
    5. Ahlswede, R, “General theory of information transfer: Updated”, Discrete Applied Mathematics, 156:9 (2008), 1348  crossref  isi
    6. V. M. Sidel'nikov, O. Yu. Prikhodov, “On the construction of $(w,r)$ cover-free codes”, Problems Inform. Transmission, 45:1 (2009), 32–36  mathnet  crossref  mathscinet  zmath  isi
    7. V. S. Lebedev, “Separating codes and a new combinatorial search model”, Problems Inform. Transmission, 46:1 (2010), 1–6  mathnet  crossref  mathscinet  isi
    8. L. A. Sholomov, “Dvoichnye predstavleniya nedoopredelennykh dannykh i diz'yunktivnye kody”, PDM, 2013, no. 1(19), 17–33  mathnet
    9. L. A. Bassalygo, V. V. Rykov, “Multiple-access hyperchannel”, Problems Inform. Transmission, 49:4 (2013), 299–307  mathnet  crossref  isi  elib
    10. 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  mathnet  crossref  isi
    11. 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  isi
    12. A. G. D'yachkov, I. V. Vorob'ev, N. A. Polyansky, V. Yu. Shchukin, “Almost disjunctive list-decoding codes”, Problems Inform. Transmission, 51:2 (2015), 110–131  mathnet  crossref  isi  elib
    13. Laarhoven T., “Asymptotics of Fingerprinting and Group Testing: Tight Bounds From Channel Capacities”, IEEE Trans. Inf. Forensic Secur., 10:9 (2015), 1967–1980  crossref  isi  elib
    14. N. A. Polyansky, “Almost cover-free codes”, Problems Inform. Transmission, 52:2 (2016), 142–155  mathnet  crossref  mathscinet  isi  elib  elib
    15. Barg A., Mazumdar A., “Group Testing Schemes From Codes and Designs”, IEEE Trans. Inf. Theory, 63:11 (2017), 7131–7141  crossref  isi
    16. De Bonis A. Vaccaro U., “Epsilon-Almost Selectors and Their Applications to Multiple-Access Communication”, IEEE Trans. Inf. Theory, 63:11 (2017), 7304–7319  crossref  isi
    17. Bshouty N.H. Gabizon A., “Almost Optimal Cover-Free Families”, Algorithms and Complexity (Ciac 2017), Lecture Notes in Computer Science, 10236, ed. Fotakis D. Pagourtzis A. Paschos V., Springer International Publishing Ag, 2017, 140–151  crossref  isi
    18. De Bonis A. Vaccaro U., “A New Kind of Selectors and Their Applications to Conflict Resolution in Wireless Multichannels Networks”, Algorithms For Sensor Systems (Algosensors 2016), Lecture Notes in Computer Science, 10050, ed. Chrobak M. Anta A. Gasieniec L. Klasing R., Springer International Publishing Ag, 2017, 45–61  crossref  isi
    19. Aldridge M., Baldassini L., Gunderson K., “Almost Separable Matrices”, J. Comb. Optim., 33:1 (2017), 215–236  crossref  isi
    20. Tsunoda Yu., Fujiwara Yu., Ando H., Vandendriessche P., “Bounds on Separating Redundancy of Linear Codes and Rates of X-Codes”, IEEE Trans. Inf. Theory, 64:12 (2018), 7577–7593  crossref  mathscinet  zmath  isi  scopus
    21. Bshouty N.H., “Exact Learning From An Honest Teacher That Answers Membership Queries”, Theor. Comput. Sci., 733:SI (2018), 4–43  crossref  mathscinet  zmath  isi  scopus
    22. Motlagh M.A., Moazami F., “A Generalization of (2, W; D)-Cover Free Families”, ARS Comb., 137 (2018), 233–248  mathscinet  zmath  isi
    23. E. E. Egorova, “Generalization of IPP codes and IPP set systems”, Problems Inform. Transmission, 55:3 (2019), 241–253  mathnet  crossref  crossref  isi  elib
    24. G. A. Kabatiansky, “Traceability codes and their generalizations”, Problems Inform. Transmission, 55:3 (2019), 283–294  mathnet  crossref  crossref  isi  elib
    25. D'yachkov A., Polyanski N., Shchukin V., Vorobyev I., “Hypothesis Test For Bounds on the Size of Random Defective Set”, IEEE Trans. Signal Process., 67:22 (2019), 5775–5784  crossref  mathscinet  zmath  isi  scopus
    26. Johnson O., Aldridge M., Scarlett J., “Performance of Group Testing Algorithms With Near-Constant Tests Per Item”, IEEE Trans. Inf. Theory, 65:2 (2019), 707–723  crossref  mathscinet  zmath  isi  scopus
    27. Vorobyev I., “a New Algorithm For Two-Stage Group Testing”, 2019 IEEE International Symposium on Information Theory (Isit), IEEE International Symposium on Information Theory, IEEE, 2019, 101–105  isi
    28. E. E. Egorova, M. Fernandes, G. A. Kabatyanskii, I. Myao, “Suschestvovanie i konstruktsii multimediinykh kodov, sposobnykh nakhodit polnuyu koalitsiyu pri atake usredneniya i shume”, Probl. peredachi inform., 56:4 (2020), 97–108  mathnet  crossref
    29. De Bonis A., Vaccaro U., “a New Kind of Selectors and Their Applications to Conflict Resolution in Wireless Multichannels Networks”, Theor. Comput. Sci., 806 (2020), 219–235  crossref  mathscinet  zmath  isi  scopus
    30. Egorova E., Fernandez M., Kabatiansky G., “on Non-Binary Traceability Set Systems”, Designs Codes Cryptogr., 88:9, SI (2020), 1885–1892  crossref  mathscinet  zmath  isi  scopus
    31. Gargano L., Rescigno A.A., Vaccaro U., “Low-Weight Superimposed Codes and Related Combinatorial Structures: Bounds and Applications”, Theor. Comput. Sci., 806 (2020), 655–672  crossref  mathscinet  zmath  isi  scopus
    32. E. E. Egorova, G. A. Kabatyanskii, “Razdelimye kody dlya zaschity multimedia ot nelegalnogo kopirovaniya koalitsiyami”, Probl. peredachi inform., 57:2 (2021), 90–111  mathnet  crossref
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