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.
%0 Journal Article
%1 leung05
%A Leung, Ka Hin
%A Schmidt, Bernhard
%D 2005
%J Designs, Codes and Cryptography
%K circulant hadamard matrix
%N 2
%P 171--188
%R 10.1007/s10623-004-1703-7
%T The Field Descent Method
%V 36
%X 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.
@article{leung05,
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.},
added-at = {2016-09-11T14:13:23.000+0200},
author = {Leung, Ka Hin and Schmidt, Bernhard},
biburl = {https://www.bibsonomy.org/bibtex/2f201608ea1a38bf8b2f4f42af02d1fe2/ytyoun},
doi = {10.1007/s10623-004-1703-7},
interhash = {9229747704b92b167eac5f4475f0d88f},
intrahash = {f201608ea1a38bf8b2f4f42af02d1fe2},
issn = {1573-7586},
journal = {Designs, Codes and Cryptography},
keywords = {circulant hadamard matrix},
number = 2,
pages = {171--188},
timestamp = {2016-10-01T08:30:52.000+0200},
title = {The Field Descent Method},
volume = 36,
year = 2005
}