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Diskretn. Anal. Issled. Oper., Ser. 1, 2006, Volume 13, Number 1, Pages 77–98 (Mi da25)  

This article is cited in 7 scientific papers (total in 7 papers)

On enumeration of nonequivalent perfect binary codes of length 15 and rank 15

S. A. Malyugin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: All nonequivalent perfect binary codes of length 15 and rank 15 are constructed that are obtained from the Hamming code $H^{15}$ by translating its disjoint components. Also, the main invariants of this class of codes are determined such as the ranks, dimensions of kernels, and orders of automorphism groups.

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English version:
Journal of Applied and Industrial Mathematics, 2007, 1:1, 77–89

Bibliographic databases:

UDC: 519.72
Received: 11.11.2005

Citation: S. A. Malyugin, “On enumeration of nonequivalent perfect binary codes of length 15 and rank 15”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:1 (2006), 77–98; J. Appl. Industr. Math., 1:1 (2007), 77–89

Citation in format AMSBIB
\Bibitem{Mal06}
\by S.~A.~Malyugin
\paper On enumeration of nonequivalent perfect binary codes of length~15 and rank~15
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2006
\vol 13
\issue 1
\pages 77--98
\mathnet{http://mi.mathnet.ru/da25}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2258905}
\zmath{https://zbmath.org/?q=an:1249.94060}
\transl
\jour J. Appl. Industr. Math.
\yr 2007
\vol 1
\issue 1
\pages 77--89
\crossref{https://doi.org/10.1134/S1990478907010085}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67849122764}


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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. Yu. L. Vasil'ev, S. V. Avgustinovich, D. S. Krotov, “On mobile sets in the binary hypercube”, J. Appl. Industr. Math., 3:2 (2009), 290–296  mathnet  crossref  mathscinet  zmath
    3. Östergård 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  zmath  isi  scopus
    4. Ostergard P.R.J., “Switching codes and designs”, Discrete Math, 312:3 (2012), 621–632  crossref  mathscinet  zmath  isi  elib  scopus
    5. S. A. Malyugin, “Affine nonsystematic codes”, J. Appl. Industr. Math., 6:4 (2012), 451–459  mathnet  crossref  mathscinet
    6. S. A. Malyugin, “Affine $3$-nonsystematic codes”, J. Appl. Industr. Math., 8:4 (2014), 552–556  mathnet  crossref  mathscinet
    7. S. A. Malyugin, “Affine $3$-nonsystematic perfect codes of length 15”, J. Appl. Industr. Math., 9:2 (2015), 251–262  mathnet  crossref  crossref  mathscinet  elib
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