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Symplectic Spreads and Permutation Polynomials

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Finite Fields and Applications (Fq 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2948))

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Abstract

Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF(q) and conversely. This leads to an algebraic proof of the existence of the Tits-Lüneburg spread of W(22h + 1) and the Ree-Tits spread of W(32h + 1), as well as to a new family of low-degree permutation polynomials over GF(32h + 1).

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Author information

Authors and Affiliations

  1. Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Mòdul C3, Campus Nord, 08034, Barcelona, Spain

    Simeon Ball

  2. Center for Communications Research, 805 Bunn Drive, Princeton, NJ, 08540–1966, USA

    Michael Zieve

Authors
  1. Simeon Ball
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  2. Michael Zieve
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, PA, USA

    Gary L. Mullen

  2. University Paul Sabatier, AAECC/IRIT, 118 route de Narbonne, 31300, Toulouse cedex, France

    Alain Poli

  3. Sabancı University - FENS, Orhanli - Tuzla, 34956, Istanbul, Turkey

    Henning Stichtenoth

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Ball, S., Zieve, M. (2004). Symplectic Spreads and Permutation Polynomials. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_7

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  • DOI: https://doi.org/10.1007/978-3-540-24633-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21324-6

  • Online ISBN: 978-3-540-24633-6

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