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Sibirsk. Mat. Zh., 2008, Volume 49, Number 2, Pages 464–474 (Mi smj1853)  

This article is cited in 2 scientific papers (total in 2 papers)

Intersections of $q$-ary perfect codes

F. I. Solov'eva, A. V. Los'

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

Abstract: The intersections of $q$-ary perfect codes are under study. We prove that there exist two $q$-ary perfect codes $C_1$ and $C_2$ of length $N=qn+1$ such that $|C_1\cap C_2|=k\cdot|P_i|/p$ for each $k\in\{0,…,p\cdot K-2,p\cdot K\}$, where $q=p^r$, $p$ is prime, $r\ge1$, $n=\dfrac{q^{m-1}-1}{q-1}$, $m\ge2$, $|P_i|=p^{nr(q-2)+n}$ and $K=p^{n(2r-1)-r(m-1)}$. We show also that there exist two $q$-ary perfect codes of length $N$ which are intersected by $p^{nr(q-3)+n}$ codewords.

Keywords: $q$-ary perfect codes, intersection of codes, switching of components, Hamming code.

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English version:
Siberian Mathematical Journal, 2008, 49:2, 375–382

Bibliographic databases:

UDC: 519.725
Received: 09.04.2007

Citation: F. I. Solov'eva, A. V. Los', “Intersections of $q$-ary perfect codes”, Sibirsk. Mat. Zh., 49:2 (2008), 464–474; Siberian Math. J., 49:2 (2008), 375–382

Citation in format AMSBIB
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\by F.~I.~Solov'eva, A.~V.~Los'
\paper Intersections of $q$-ary perfect codes
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 2
\pages 464--474
\mathnet{http://mi.mathnet.ru/smj1853}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2419668}
\zmath{https://zbmath.org/?q=an:1155.94407}
\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 2
\pages 375--382
\crossref{https://doi.org/10.1007/s11202-008-0036-6}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-43349097902}


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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. Rifà J., Solov'eva F.I., Villanueva M., “On the intersection of $\mathbb Z_2\mathbb Z_4$-additive Hadamard codes”, IEEE Trans. Inform. Theory, 55:4 (2009), 1766–1774  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Problems Inform. Transmission, 48:1 (2012), 47–55  mathnet  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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