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Probl. Peredachi Inf., 2009, Volume 45, Issue 2, Pages 78–83 (Mi ppi1979)  

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

Coding Theory

On weak isometries of Preparata codes

I. Yu. Mogil'nykh

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

Abstract: Two codes $C_1$ and $C_2$ are said to be weakly isometric if there exists a mapping $J\colon C_1\to C_2$ such that for all $x,y$ in $C_1$ the equality $d(x,y)=d$ holds if and only if $d(J(x),J(y))=d$, where $d$ is the code distance of $C_1$. We prove that Preparata codes of length $n\ge2^{12}$ are weakly isometric if and only if the codes are equivalent. A similar result is proved for punctured Preparata codes of length at least $2^{10}-1$.

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English version:
Problems of Information Transmission, 2009, 45:2, 145–150

Bibliographic databases:

UDC: 621.391.15
Received: 11.01.2009
Revised: 17.03.2009

Citation: I. Yu. Mogil'nykh, “On weak isometries of Preparata codes”, Probl. Peredachi Inf., 45:2 (2009), 78–83; Problems Inform. Transmission, 45:2 (2009), 145–150

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. Fernández-Córdoba C., Phelps K.T., “On the minimum distance graph of an extended Preparata code”, Des. Codes Cryptogr., 57:2 (2010), 161–168  crossref  mathscinet  zmath  isi  elib
    3. 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
    4. Romanov A.M., “Disjoint Hamiltonian Cycles in Minimum Distance Graphs of 1-Perfect Codes”, Australas. J. Comb., 69:2 (2017), 215–221  mathscinet  zmath  isi
  • Проблемы передачи информации Problems of Information Transmission
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