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Complete Systems of Lines on a Hermitian Surface over a Finite Field

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Abstract

The aim is to find the maximum size of a set of mutually ske lines on a nonsingular Hermitian surface in PG(3, q) for various values of q. For q = 9 such extremal sets are intricate combinatorial structures intimately connected ith hemisystems, subreguli, and commuting null polarities. It turns out they are also closely related to the classical quartic surface of Kummer. Some bounds and examples are also given in the general case.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaare, Neark, Delaware, 19716, U.S.A

    G. L. Ebert

  2. School of Mathematical Sciences, University of Sussex, Brighton, East Sussex, BN1 9QH, U.K

    J. W. P. Hirschfeld

Authors
  1. G. L. Ebert
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  2. J. W. P. Hirschfeld
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Ebert, G.L., Hirschfeld, J.W.P. Complete Systems of Lines on a Hermitian Surface over a Finite Field. Designs, Codes and Cryptography 17, 253–268 (1999). https://doi.org/10.1023/A:1026439528939

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  • DOI: https://doi.org/10.1023/A:1026439528939

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