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Probl. Peredachi Inf., 2004, Volume 40, Issue 1, Pages 27–39 (Mi ppi121)  

This article is cited in 9 scientific papers (total in 9 papers)

Coding Theory

Binary Perfect Codes of Length 15 by Generalized Concatenated Construction

V. A. Zinov'ev, D. V. Zinov'ev

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We enumerate binary nonlinear perfect codes of length 15 obtained by the generalized concatenated (GC) construction. There are 15 different types of such codes. They are defined by pairs of MDS codes $A_i$: $(4,2,64)_4$. For every pair we give the number of nonequivalent codes of this type. In total, there are 777 nonequivalent binary perfect codes of length 15 obtained by the GC construction. This number includes the Hamming code (of rank 11), 18 Vasil'ev codes (of rank 12), and 758 codes of rank 13.

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English version:
Problems of Information Transmission, 2004, 40:1, 25–36

Bibliographic databases:

UDC: 621.391.15
Received: 18.06.2003

Citation: V. A. Zinov'ev, D. V. Zinov'ev, “Binary Perfect Codes of Length 15 by Generalized Concatenated Construction”, Probl. Peredachi Inf., 40:1 (2004), 27–39; Problems Inform. Transmission, 40:1 (2004), 25–36

Citation in format AMSBIB
\Bibitem{ZinZin04}
\by V.~A.~Zinov'ev, D.~V.~Zinov'ev
\paper Binary Perfect Codes of Length~15 by Generalized Concatenated Construction
\jour Probl. Peredachi Inf.
\yr 2004
\vol 40
\issue 1
\pages 27--39
\mathnet{http://mi.mathnet.ru/ppi121}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099017}
\zmath{https://zbmath.org/?q=an:1084.94022}
\transl
\jour Problems Inform. Transmission
\yr 2004
\vol 40
\issue 1
\pages 25--36
\crossref{https://doi.org/10.1023/B:PRIT.0000024877.03232.39}


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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. A. M. Romanov, “A survey of methods for constructing nonlinear perfect binary codes”, J. Appl. Industr. Math., 2:2 (2008), 252–269  mathnet  crossref  mathscinet  zmath
    2. S. A. Malyugin, “On enumeration of nonequivalent perfect binary codes of length 15 and rank 15”, J. Appl. Industr. Math., 1:1 (2007), 77–89  mathnet  crossref  mathscinet  zmath
    3. V. A. Zinov'ev, D. V. Zinov'ev, “Vasil'ev Codes of Length $n=2^m$ and Doubling of Steiner Systems $S(n,4,3)$ of a Given Rank”, Problems Inform. Transmission, 42:1 (2006), 10–29  mathnet  crossref  mathscinet  zmath
    4. V. A. Zinov'ev, D. V. Zinov'ev, “Binary Extended Perfect Codes of Length 16 and Rank 14”, Problems Inform. Transmission, 42:2 (2006), 123–138  mathnet  crossref  mathscinet
    5. Heden O., “A survey of perfect codes”, Adv. Math. Commun., 2:2 (2008), 223–247  crossref  mathscinet  zmath  isi  elib
    6. Solov'eva F.I., “On perfect binary codes”, Discrete Appl. Math., 156:9 (2008), 1488–1498  crossref  mathscinet  zmath  isi
    7. V. A. Zinoviev, D. V. Zinoviev, “Binary perfect and extended perfect codes of lengths 15 and 16 with ranks 13 and 14”, Problems Inform. Transmission, 46:1 (2010), 17–21  mathnet  crossref  mathscinet  isi
    8. Ostergard P.R.J., Pottonen O., Phelps K.T., “The Perfect Binary One-Error-Correcting Codes of Length 15: Part II-Properties”, IEEE Trans Inform Theory, 56:6 (2010), 2571–2582  crossref  mathscinet  isi  elib
    9. Heden O., Hessler M., Westerback T., “On the classification of perfect codes: Extended side class structures”, Discrete Math, 310:1 (2010), 43–55  crossref  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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