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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 3, Pages 668–681 (Mi smj1869)  

This article is cited in 1 scientific paper (total in 1 paper)

Distance regularity of Kerdock codes

F. I. Solov'eva, N. N. Tokareva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (343 kB) Citations (1)
References:
Abstract: A code is called distance regular, if for every two codewords $\mathbf x,\mathbf y$ and integers $i,j$ the number of codewords $\mathbf z$ such that $d(\mathbf x,\mathbf z)=i$ and $d(\mathbf y,\mathbf z)=j$, with $d$ the Hamming distance, does not depend on the choice of $\mathbf x,\mathbf y$ and depends only on $d(\mathbf x,\mathbf y)$ and $i,j$. Using some properties of the discrete Fourier transform we give a new combinatorial proof of the distance regularity of an arbitrary Kerdock code. We also calculate the parameters of the distance regularity of a Kerdock code.
Keywords: distance regular code, Kerdock code, Reed–Muller code, discrete Fourier transform, bent function, distance regular graph, association scheme.
Received: 30.05.2006
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 3, Pages 539–548
DOI: https://doi.org/10.1007/s11202-008-0051-7
Bibliographic databases:
UDC: 519.725
Language: Russian
Citation: F. I. Solov'eva, N. N. Tokareva, “Distance regularity of Kerdock codes”, Sibirsk. Mat. Zh., 49:3 (2008), 668–681; Siberian Math. J., 49:3 (2008), 539–548
Citation in format AMSBIB
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\by F.~I.~Solov'eva, N.~N.~Tokareva
\paper Distance regularity of Kerdock codes
\jour Sibirsk. Mat. Zh.
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\vol 49
\issue 3
\pages 668--681
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\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 3
\pages 539--548
\crossref{https://doi.org/10.1007/s11202-008-0051-7}
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  • https://www.mathnet.ru/eng/smj/v49/i3/p668
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Full-text PDF :84
    References:45
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