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

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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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Authors and Affiliations

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

    M. E. Kovalenko & T. A. Urbanovich

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  1. M. E. Kovalenko
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  2. T. A. Urbanovich
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Correspondence to M. E. Kovalenko.

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Original Russian Text © M.E. Kovalenko, T.A. Urbanovich, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 1, pp. 87–97.

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Kovalenko, M.E., Urbanovich, T.A. On the rank of incidence matrices for points and lines of finite affine and projective geometries over a field of four elements. Probl Inf Transm 50, 79–89 (2014). https://doi.org/10.1134/S0032946014010050

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  • DOI: https://doi.org/10.1134/S0032946014010050

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