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Probl. Peredachi Inf., 2005, Volume 41, Issue 2, Pages 50–62 (Mi ppi95)  

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

Coding Theory

Representation of $\mathbb Z_4$-Linear Preparata Codes by Means of Vector Fields

N. N. Tokareva

Novosibirsk State University

Abstract: A binary code is called $\mathbb Z_4$-linear if its quaternary Gray map preimage is linear. We show that the set of all quaternary linear Preparata codes of length $n=2^m$, $m$ odd, $m\ge3$, is nothing more than the set of codes of the form $\mathcal H_{\lambda,\psi}+\mathcal M$ with
$$ \mathcal H_{\lambda,\psi}=\{y+T_\lambda(y)+S_\psi(y)\mid y\in H^n\},\qquad \mathcal M=2H^n, $$
where $T_\lambda( \cdot )$ and $S_\psi( \cdot )$ are vector fields of a special form defined over the binary extended linear Hamming code $H^n$ of length $n$. An upper bound on the number of nonequivalent quaternary linear Preparata codes of length $n$ is obtained, namely, $2^{n\log_2n}$. A representation for binary Preparata codes contained in perfect Vasil'ev codes is suggested.

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English version:
Problems of Information Transmission, 2005, 41:2, 113–124

Bibliographic databases:

UDC: 621.391.15
Received: 08.12.2004
Revised: 14.03.2005

Citation: N. N. Tokareva, “Representation of $\mathbb Z_4$-Linear Preparata Codes by Means of Vector Fields”, Probl. Peredachi Inf., 41:2 (2005), 50–62; Problems Inform. Transmission, 41:2 (2005), 113–124

Citation in format AMSBIB
\Bibitem{Tok05}
\by N.~N.~Tokareva
\paper Representation of $\mathbb Z_4$-Linear Preparata Codes by Means of Vector Fields
\jour Probl. Peredachi Inf.
\yr 2005
\vol 41
\issue 2
\pages 50--62
\mathnet{http://mi.mathnet.ru/ppi95}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2158684}
\zmath{https://zbmath.org/?q=an:1088.94029}
\transl
\jour Problems Inform. Transmission
\yr 2005
\vol 41
\issue 2
\pages 113--124
\crossref{https://doi.org/10.1007/s11122-005-0016-4}


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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. J. Appl. Industr. Math., 2:3 (2008), 426–431  mathnet  crossref  mathscinet  zmath
    2. F. I. Solov'eva, “On $\mathbb Z_4$-Linear Codes with Parameters of Reed–Muller Codes”, Problems Inform. Transmission, 43:1 (2007), 26–32  mathnet  crossref  mathscinet  isi  elib  elib
    3. Tokareva N., “An upper bound for the number of uniformly packed codes”, 2007 IEEE International Symposium on Information Theory Proceedings, 2007, 346–349  crossref  isi
    4. Krotov D.S., “On diameter perfect constant-weight ternary codes”, Discrete Math., 308:14 (2008), 3104–3114  crossref  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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