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Probl. Peredachi Inf., 2003, Volume 39, Issue 2, Pages 23–28 (Mi ppi214)  

This article is cited in 8 scientific papers (total in 8 papers)

Information Theory and Coding Theory

To Metric Rigidity of Binary Codes

S. V. Avgustinovich, F. I. Solov'eva


Abstract: A code $C$ in the $n$-dimensional metric space $E^n$ over $GF(2)$ is called metrically rigid if each isometry $I\colon C\to E^n$ can be extended to an isometry of the whole space $E^n$. For $n$ large enough, metrical rigidity of any length-$n$ binary code that contains a $2-(n,k,\lambda)$–design is proved. The class of such codes includes, for instance, all families of uniformly packed codes of large enough lengths that satisfy the condition $d-\rho\geq 2$, where $d$ is the code distance and $\rho$ is the covering radius.

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English version:
Problems of Information Transmission, 2003, 39:2, 178–183

Bibliographic databases:

UDC: 621.391.15
Received: 14.06.2002
Revised: 04.09.2002

Citation: S. V. Avgustinovich, F. I. Solov'eva, “To Metric Rigidity of Binary Codes”, Probl. Peredachi Inf., 39:2 (2003), 23–28; Problems Inform. Transmission, 39:2 (2003), 178–183

Citation in format AMSBIB
\Bibitem{AvgSol03}
\by S.~V.~Avgustinovich, F.~I.~Solov'eva
\paper To Metric Rigidity of Binary Codes
\jour Probl. Peredachi Inf.
\yr 2003
\vol 39
\issue 2
\pages 23--28
\mathnet{http://mi.mathnet.ru/ppi214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2105858}
\zmath{https://zbmath.org/?q=an:1089.94039}
\transl
\jour Problems Inform. Transmission
\yr 2003
\vol 39
\issue 2
\pages 178--183
\crossref{https://doi.org/10.1023/A:1025148221096}


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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. I. Yu. Mogil'nykh, “On weak isometries of Preparata codes”, Problems Inform. Transmission, 45:2 (2009), 145–150  mathnet  crossref  mathscinet  zmath  isi
    2. Mogilnykh, IY, “Reconstructing Extended Perfect Binary One-Error-Correcting Codes From Their Minimum Distance Graphs”, IEEE Transactions on Information Theory, 55:6 (2009), 2622  crossref  mathscinet  isi
    3. E. V. Gorkunov, S. V. Avgustinovich, “On reconstruction of binary codes by dimensions of their subcodes”, J. Appl. Industr. Math., 5:3 (2011), 348–351  mathnet  crossref  mathscinet  zmath
    4. D. I. Kovalevskaya, “On metric rigidity for some classes of codes”, Problems Inform. Transmission, 47:1 (2011), 15–27  mathnet  crossref  mathscinet  isi
    5. S. V. Avgustinovich, E. V. Gorkunov, “On reconstruction of a binary code from dimensions of its subcodes”, J. Appl. Industr. Math., 7:2 (2013), 127–130  mathnet  crossref  mathscinet
    6. I. Yu. Mogil'nykh, “On extending propelinear structures of the Nordstrom–Robinson code to the Hamming code”, Problems Inform. Transmission, 52:3 (2016), 289–298  mathnet  crossref  isi  elib
    7. Dyshko S., “Macwilliams Extension Theorem For Mds Codes Over a Vector Space Alphabet”, Designs Codes Cryptogr., 82:1-2, SI (2017), 57–67  crossref  mathscinet  zmath  isi  scopus
    8. Dyshko S., “Isometry Groups of Combinatorial Codes”, J. Algebra. Appl., 17:6 (2018), 1850114  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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