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Diskretn. Anal. Issled. Oper., Ser. 1, 2006, Volume 13, Number 4, Pages 60–88 (Mi da12)  

This article is cited in 4 scientific papers (total in 4 papers)

A survey of methods for constructing nonlinear perfect binary codes

A. M. Romanov

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

Abstract: The theory of perfect codes is an area at the juncture of coding theory and design theory which is rather hard to explore. Linear perfect codes were constructed by M. Golay and R. Hamming in the end of the 1940s. Nonlinear perfect codes were discovered by Yu. L. Vasil'ev in 1961. At present, many different methods are known for constructing perfect codes. This article presents a survey of the methods for constructing nonlinear perfect binary codes alongside some open questions of the theory of perfect codes.

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English version:
Journal of Applied and Industrial Mathematics, 2008, 2:2, 252–269

Bibliographic databases:


Citation: A. M. Romanov, “A survey of methods for constructing nonlinear perfect binary codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:4 (2006), 60–88; J. Appl. Industr. Math., 2:2 (2008), 252–269

Citation in format AMSBIB
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\by A.~M.~Romanov
\paper A survey of methods for constructing nonlinear perfect binary codes
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2006
\vol 13
\issue 4
\pages 60--88
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2289379}
\zmath{https://zbmath.org/?q=an:1249.94051}
\transl
\jour J. Appl. Industr. Math.
\yr 2008
\vol 2
\issue 2
\pages 252--269
\crossref{https://doi.org/10.1134/S1990478908020105}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-44949201467}


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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, “On combinatorial Gray codes with distance 3”, Discrete Math. Appl., 19:4 (2009), 383–388  mathnet  crossref  crossref  mathscinet  elib
    2. D. S. Krotov, V. N. Potapov, “On switching equivalence of $n$-ary quasigroups of order 4 and perfect binary codes”, Problems Inform. Transmission, 46:3 (2010), 219–224  mathnet  crossref  mathscinet  isi
    3. A. M. Romanov, “On full-rank perfect codes over finite fields”, J. Appl. Industr. Math., 10:3 (2016), 444–452  mathnet  crossref  crossref  mathscinet  elib
    4. A. M. Romanov, “On the embedding of constant-weight codes into perfect codes”, J. Appl. Industr. Math., 10:4 (2016), 556–559  mathnet  crossref  crossref  mathscinet  elib
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