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2-Ranks of incidence matrices associated with conics in finite projective planes

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Abstract

In this article, we investigate geometric properties of the secant-internal neighbors of internal points and the passant-external neighbors of external points in classical finite projective planes; we calculate the \(2\)-ranks of the incidence matrices of internal points versus their secant-internal neighbors and external points versus their passant-external neighbors using a combination of techniques from both finite geometry and linear algebra.

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Acknowledgments

This research was supported in part by NSF HBCU-UP Grant Award \(0929257\) at Lane College.

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Authors and Affiliations

  1. Department of Mathematics, Lane College, Jackson, TN, USA

    Megan Adams & Junhua Wu

Authors
  1. Megan Adams
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  2. Junhua Wu
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Correspondence to Megan Adams.

Additional information

Communicated by J. W. P. Hirschfeld.

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Adams, M., Wu, J. 2-Ranks of incidence matrices associated with conics in finite projective planes. Des. Codes Cryptogr. 72, 381–404 (2014). https://doi.org/10.1007/s10623-012-9772-5

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  • DOI: https://doi.org/10.1007/s10623-012-9772-5

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