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Probl. Peredachi Inf., 2014, Volume 50, Issue 1, Pages 87–97 (Mi ppi2133)  

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

Large Systems

On the rank of incidence matrices for points and lines of finite affine and projective geometries over a field of four elements

M. E. Kovalenko, T. A. Urbanovich

Discrete Mathematics Chair, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider incidence matrices for points and lines of affine and projective geometries over a field of four elements. For such matrices we derive a simple formula for the $2$-rank and, as a consequence, new combinatorial identities expressing the relation of the obtained formulas for the rank with previously known formulas. We also present a way to construct generating systems for rows of these matrices.

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English version:
Problems of Information Transmission, 2014, 50:1, 79–89

Bibliographic databases:

UDC: 621.391.1+512
Received: 04.09.2013
Revised: 20.01.2014

Citation: M. E. Kovalenko, T. A. Urbanovich, “On the rank of incidence matrices for points and lines of finite affine and projective geometries over a field of four elements”, Probl. Peredachi Inf., 50:1 (2014), 87–97; Problems Inform. Transmission, 50:1 (2014), 79–89

Citation in format AMSBIB
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\by M.~E.~Kovalenko, T.~A.~Urbanovich
\paper On the rank of incidence matrices for points and lines of finite affine and projective geometries over a~field of four elements
\jour Probl. Peredachi Inf.
\yr 2014
\vol 50
\issue 1
\pages 87--97
\mathnet{http://mi.mathnet.ru/ppi2133}
\transl
\jour Problems Inform. Transmission
\yr 2014
\vol 50
\issue 1
\pages 79--89
\crossref{https://doi.org/10.1134/S0032946014010050}
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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. M. E. Kovalenko, “O radiuse pokrytiya lineinykh kodov, porozhdennykh affinnymi geometriyami nad polem iz chetyrekh elementov”, PDM, 2014, no. 4(26), 72–77  mathnet
  • Проблемы передачи информации Problems of Information Transmission
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