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Problemy Peredachi Informatsii, 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
References:
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.
Received: 08.12.2004
Revised: 14.03.2005
English version:
Problems of Information Transmission, 2005, Volume 41, Issue 2, Pages 113–124
DOI: https://doi.org/10.1007/s11122-005-0016-4
Bibliographic databases:
Document Type: Article
UDC: 621.391.15
Language: Russian
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://mathscinet.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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  • https://www.mathnet.ru/eng/ppi/v41/i2/p50
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Проблемы передачи информации Problems of Information Transmission
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