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Probl. Peredachi Inf., 2017, Volume 53, Issue 2, Pages 40–59 (Mi ppi2234)  

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

Coding Theory

MDS codes in Doob graphs

E. A. Bespalov, D. S. Krotov

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

Abstract: The Doob graph $D(m,n)$, where $m>0$, is a Cartesian product of $m$ copies of the Shrikhande graph and $n$ copies of the complete graph $K_4$ on four vertices. The Doob graph $D(m,n)$ is a distance-regular graph with the same parameters as the Hamming graph $H(2m+n,4)$. We give a characterization of MDS codes in Doob graphs $D(m,n)$ with code distance at least $3$. Up to equivalence, there are $m^3/36+7m^2/24+11m/12+1-(m\bmod2)/8-(m\bmod3)/9$ MDS codes with code distance $2m+n$ in $D(m,n)$, two codes with distance $3$ in each of $D(2,0)$ and $D(2,1)$ and with distance $4$ in $D(2,1)$, and one code with distance $3$ in each of $D(1,2)$ and $D(1,3)$ and with distance $4$ in each of $D(1,3)$ and $D(2,2)$.

Funding Agency Grant Number
Russian Science Foundation 14-11-00555
The research was carried out at the expense of the Russian Science Foundation, project no. 14-11-00555.


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English version:
Problems of Information Transmission, 2017, 53:2, 136–154

Bibliographic databases:

UDC: 621.391.15
Received: 06.02.2016
Revised: 04.12.2016

Citation: E. A. Bespalov, D. S. Krotov, “MDS codes in Doob graphs”, Probl. Peredachi Inf., 53:2 (2017), 40–59; Problems Inform. Transmission, 53:2 (2017), 136–154

Citation in format AMSBIB
\Bibitem{BesKro17}
\by E.~A.~Bespalov, D.~S.~Krotov
\paper MDS codes in Doob graphs
\jour Probl. Peredachi Inf.
\yr 2017
\vol 53
\issue 2
\pages 40--59
\mathnet{http://mi.mathnet.ru/ppi2234}
\elib{http://elibrary.ru/item.asp?id=29202067}
\transl
\jour Problems Inform. Transmission
\yr 2017
\vol 53
\issue 2
\pages 136--154
\crossref{https://doi.org/10.1134/S003294601702003X}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85023769057}


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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. E. A. Bespalov, “On the minimum supports of some eigenfunctions in the Doob graphs”, Sib. elektron. matem. izv., 15 (2018), 258–266  mathnet  crossref
    2. D. S. Krotov, E. A. Bespalov, “Distance-2 MDS codes and Latin colorings in the Doob graphs”, Graphs Comb., 34:5 (2018), 1001–1017  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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