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Mat. Zametki, 2012, Volume 91, Issue 5, Pages 741–749 (Mi mz9362)  

This article is cited in 3 scientific papers (total in 3 papers)

Classification of $(v,3)$-Configurations

F. M. Malyshev, A. A. Frolov

Academy of Criptography of Russia

Abstract: A $(v,3)$-configuration is a nondegenerate matrix of dimension $v$ over the field $\mathrm{GF}(2)$ considered up to permutation of rows and columns and containing exactly three $1$'s in the rows and columns, while the inverse matrix has also exactly three $1$'s in the rows and columns. It is proved that, for each even $v\ge 4$, there is only one indecomposable $(v,3)$-configuration, while, for odd $v$, there are no such configurations, the only exception being the unique $(5,3)$-configuration.

Keywords: $(v,3)$-configuration, nondegenerate matrix, Möbius strip

DOI: https://doi.org/10.4213/mzm9362

Full text: PDF file (506 kB)
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English version:
Mathematical Notes, 2012, 91:5, 689–696

Bibliographic databases:

Document Type: Article
UDC: 519.142.1
Received: 12.11.2010

Citation: F. M. Malyshev, A. A. Frolov, “Classification of $(v,3)$-Configurations”, Mat. Zametki, 91:5 (2012), 741–749; Math. Notes, 91:5 (2012), 689–696

Citation in format AMSBIB
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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. F. M. Malyshev, “Tri semeistva $5$-konfiguratsii”, Matem. vopr. kriptogr., 4:3 (2013), 83–97  mathnet  crossref
    2. F. M. Malyshev, “Chetyre beskonechnye serii $k$-konfiguratsii”, Matem. vopr. kriptogr., 4:4 (2013), 65–75  mathnet  crossref
    3. F. M. Malyshev, “Bazisy rekurrentnykh posledovatelnostei”, Chebyshevskii sb., 16:2 (2015), 155–185  mathnet  elib
  • Математические заметки Mathematical Notes
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