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3-Designs from Z4-Goethals-Like Codes and Variants of Cyclotomic Polynomials

  • Jyrki Lahtonen
  • Kalle Ranto
  • Roope Vehkalahti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)

Abstract

We construct a family of simple 3-(2 m ,8,14(2 m –8)/3) designs, with odd m≥5, from all Z 4-Goethals-like codes \({\mathcal{G}}_k\) with k=2 l and l≥1. In addition, these designs imply also the existence of the other design families constructed from the Z 4-Goethals codes \({\mathcal{G}}_1\) by Ranto. In the existence proofs we count the number of solutions to certain systems of equations over finite fields and use Dickson polynomials and variants of cyclotomic polynomials and identities connecting them.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jyrki Lahtonen
    • 1
    • 2
  • Kalle Ranto
    • 1
    • 2
  • Roope Vehkalahti
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of TurkuFinland
  2. 2.Turku Centre for Computer Science TUCSTurkuFinland

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