Designs, Codes and Cryptography

, Volume 36, Issue 2, pp 171–188 | Cite as

The Field Descent Method

  • Ka Hin Leung
  • Bernhard Schmidt


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.


difference sets field descent groups rings characters exponent bound 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Ka Hin Leung
    • 1
  • Bernhard Schmidt
    • 2
  1. 1.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore
  2. 2.Institut für MathematikUniversität AugsburgAugsburgGermany

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