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The Field Descent Method

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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 4<v<548, 964, 900 and no Barker sequence of length l with 13 < l ≤ 1022.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Kent Ridge, Singapore, 119260, Republic of Singapore

    Ka Hin Leung

  2. Institut für Mathematik, Universität Augsburg, 86135, Augsburg, Germany

    Bernhard Schmidt

Authors
  1. Ka Hin Leung
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  2. Bernhard Schmidt
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Leung, K.H., Schmidt, B. The Field Descent Method. Des Codes Crypt 36, 171–188 (2005). https://doi.org/10.1007/s10623-004-1703-7

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  • DOI: https://doi.org/10.1007/s10623-004-1703-7

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