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Probl. Peredachi Inf., 2007, Volume 43, Issue 4, Pages 45–50 (Mi ppi26)  

This article is cited in 11 scientific papers (total in 11 papers)

Coding Theory

Partitions of an $n$-Cube into Nonequivalent Perfect Codes

S. V. Avgustinovichab, F. I. Solov'evaab, O. Hedenc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
c Royal Institute of Technology

Abstract: We prove that for all $n=2^k-1$, $k\ge5$, there exists a partition of the set of all binary vectors of length $n$ into pairwise nonequivalent perfect binary codes of length $n$ with distance 3.

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English version:
Problems of Information Transmission, 2007, 43:4, 310–315

Bibliographic databases:

UDC: 621.391.15
Received: 09.04.2007
Revised: 13.09.2007

Citation: S. V. Avgustinovich, F. I. Solov'eva, O. Heden, “Partitions of an $n$-Cube into Nonequivalent Perfect Codes”, Probl. Peredachi Inf., 43:4 (2007), 45–50; Problems Inform. Transmission, 43:4 (2007), 310–315

Citation in format AMSBIB
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\by S.~V.~Avgustinovich, F.~I.~Solov'eva, O.~Heden
\paper Partitions of an $n$-Cube into Nonequivalent Perfect Codes
\jour Probl. Peredachi Inf.
\yr 2007
\vol 43
\issue 4
\pages 45--50
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\zmath{https://zbmath.org/?q=an:05319697}
\transl
\jour Problems Inform. Transmission
\yr 2007
\vol 43
\issue 4
\pages 310--315
\crossref{https://doi.org/10.1134/S0032946007040047}
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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. S. V. Avgustinovich, “Multidimensional permanents in enumrative problems”, J. Appl. Industr. Math., 4:1 (2010), 19–20  mathnet  crossref  mathscinet  zmath
    2. Heden O., “A survey of perfect codes”, Adv. Math. Commun., 2:2 (2008), 223–247  crossref  mathscinet  zmath  isi  elib
    3. F. I. Solov'eva, “On transitive partitions of an $n$-cube into codes”, Problems Inform. Transmission, 45:1 (2009), 23–31  mathnet  crossref  mathscinet  zmath  isi
    4. F. I. Solov'eva, A. V. Los', “On partitions into perfect $q$-ary codes”, J. Appl. Industr. Math., 4:1 (2010), 136–142  mathnet  crossref  mathscinet  zmath
    5. Heden O., Solov'eva F.I., “Partitions of $\mathbb F^n$ into non-parallel Hamming codes”, Adv. Math. Commun., 3:4 (2009), 385–397  crossref  mathscinet  zmath  isi  elib
    6. F. I. Soloveva, G. K. Guskov, “O postroenii vershinno-tranzitivnykh razbienii $n$-kuba na sovershennye kody”, Diskretn. analiz i issled. oper., 17:3 (2010), 84–100  mathnet  mathscinet  zmath
    7. A. V. Los, F. I. Soloveva, “O razbieniyakh prostranstva $F^N_q$ na affinno neekvivalentnye sovershennye $q$-znachnye kody”, Sib. elektron. matem. izv., 7 (2010), 425–434  mathnet
    8. A. V. Los, K. I. Burnakov, “O postroenii razbienii $(p+1)$-mernogo prostranstva vsekh $p$-znachnykh vektorov na kody Khemminga”, Sib. elektron. matem. izv., 8 (2011), 372–380  mathnet
    9. G. K. Guskov, “O razbieniyakh dvoichnogo vektornogo prostranstva na sovershennye kody”, Diskretn. analiz i issled. oper., 20:2 (2013), 15–25  mathnet  mathscinet
    10. Krotov D.S., “A Partition of the Hypercube Into Maximally Nonparallel Hamming Codes”, J. Comb Des., 22:4 (2014), 179–187  crossref  mathscinet  zmath  isi  elib
    11. S. V. Avgustinovich, E. V. Gorkunov, “Maksimalnoe peresechenie lineinykh i ekvivalentnykh im kodov”, Diskretn. analiz i issled. oper., 26:4 (2019), 5–15  mathnet  crossref
  • Проблемы передачи информации Problems of Information Transmission
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