The Field Descent Method |
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Authors: | Ka Hin Leung Bernhard Schmidt |
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Institution: | (1) Department of Mathematics, National University of Singapore, Kent Ridge, Singapore, 119260, Republic of Singapore;(2) Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany |
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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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Keywords: | difference sets field descent groups rings characters exponent bound |
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