The Field Descent Method

  • Authors:
  • Ka Hin Leung;Bernhard Schmidt

  • Affiliations:
  • Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore 119260;Institut für Mathematik, Universität Augsburg, Augsburg, Germany 86135

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2005

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Abstract

We obtain a broadly applicable decomposition of group ring elements into a "subfield part" and a "kernel part". Applications include the verification of Lander's conjecture for all difference sets whose order is a power of a prime 3 and for all McFarland, Spence and Chen/Davis/Jedwab difference sets. We obtain a new general exponent bound for difference sets. We show that there is no circulant Hadamard matrix of order v with 4vl with 13 l 驴 1022.