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Characters and cyclotomic fields in finite geometry
This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Ma...
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| Lenguaje: | eng |
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Springer
2002
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| Acceso en línea: | https://dx.doi.org/10.1007/b84213 http://cds.cern.ch/record/1691433 |
| _version_ | 1780935752213856256 |
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| author | Schmidt, Bernhard |
| author_facet | Schmidt, Bernhard |
| author_sort | Schmidt, Bernhard |
| collection | CERN |
| description | This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained. |
| id | cern-1691433 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 2002 |
| publisher | Springer |
| record_format | invenio |
| spelling | cern-16914332021-04-21T21:09:59Zdoi:10.1007/b84213http://cds.cern.ch/record/1691433engSchmidt, BernhardCharacters and cyclotomic fields in finite geometryMathematical Physics and MathematicsThis monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.Springeroai:cds.cern.ch:16914332002 |
| spellingShingle | Mathematical Physics and Mathematics Schmidt, Bernhard Characters and cyclotomic fields in finite geometry |
| title | Characters and cyclotomic fields in finite geometry |
| title_full | Characters and cyclotomic fields in finite geometry |
| title_fullStr | Characters and cyclotomic fields in finite geometry |
| title_full_unstemmed | Characters and cyclotomic fields in finite geometry |
| title_short | Characters and cyclotomic fields in finite geometry |
| title_sort | characters and cyclotomic fields in finite geometry |
| topic | Mathematical Physics and Mathematics |
| url | https://dx.doi.org/10.1007/b84213 http://cds.cern.ch/record/1691433 |
| work_keys_str_mv | AT schmidtbernhard charactersandcyclotomicfieldsinfinitegeometry |