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Characterizing the Hermitian and Ree Unitals on 28 Points

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Abstract

We prove a conjecture of Brouwer, namely that a 2-(28,4,1) design has 2–rank at least 19, with equality occuring if and only if the design is the Ree unital. We give a similar characterization of the Hermitian unital.

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Authors and Affiliations

  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Gary McGuire

  2. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Vladimir D. Tonchev

  3. Department of Mathematics, University of Virginia, Charlottesville, VA, 22903, USA

    Harold N. Ward

Authors
  1. Gary McGuire
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  2. Vladimir D. Tonchev
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  3. Harold N. Ward
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McGuire, G., Tonchev, V.D. & Ward, H.N. Characterizing the Hermitian and Ree Unitals on 28 Points. Designs, Codes and Cryptography 13, 57–61 (1998). https://doi.org/10.1023/A:1008246022572

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  • DOI: https://doi.org/10.1023/A:1008246022572

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