The field descent method
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...
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sg-ntu-dr.10356-919632023-02-28T19:36:58Z The field descent method Bernhard, Schmidt. Ka, Hin Leung. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics 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 < 10^22. Accepted version 2009-08-11T06:18:31Z 2019-12-06T18:14:54Z 2009-08-11T06:18:31Z 2019-12-06T18:14:54Z 2005 2005 Journal Article Bernhard, S., & Ka, H. L. (2005). The field descent method. Journal of designs codes and cryptography, 36(2), 171-188. 0925-1022 https://hdl.handle.net/10356/91963 http://hdl.handle.net/10220/6034 10.1007/s10623-004-1703-7 en Journal of designs codes and cryptography Designs, codes and cryptography © copyright 2005 Springer Netherlands. The journal's website is located at http://www.springerlink.com/content/lwt1482721p60t1j. 21 p. application/pdf |
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DRNTU::Science::Mathematics::Discrete mathematics::Combinatorics Bernhard, Schmidt. Ka, Hin Leung. The field descent method |
| description |
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 < 10^22. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Bernhard, Schmidt. Ka, Hin Leung. |
| format |
Article |
| author |
Bernhard, Schmidt. Ka, Hin Leung. |
| author_sort |
Bernhard, Schmidt. |
| title |
The field descent method |
| title_short |
The field descent method |
| title_full |
The field descent method |
| title_fullStr |
The field descent method |
| title_full_unstemmed |
The field descent method |
| title_sort |
field descent method |
| publishDate |
2009 |
| url |
https://hdl.handle.net/10356/91963 http://hdl.handle.net/10220/6034 |
| _version_ |
1759855515113881600 |