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...
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Serie: | Lecture notes in mathematics
1797 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Characters and cyclotomic fields in finite geometry, Bernhard Schmidt, 2002, Berlin, Springer, 1 vol. (VIII-100 p.), Lecture notes in mathematics, 3-540-44243-X • Characters and Cyclotomic Fields in Finite Geometry, Texte imprimé, 9783662183199 |
| LEADER | 03285nam a22003977a 4500 | ||
|---|---|---|---|
| 001 | 972611 | ||
| 008 | 110927q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN15522705X | ||
| 020 | |a 9783540457978 (PDF) | ||
| 041 | 0 | |a eng | |
| 082 | |a 510 | ||
| 082 | |a 516.13 | ||
| 100 | 1 | |a Schmidt, Bernhard, |d 1967- | |
| 245 | 1 | 0 | |a Characters and Cyclotomic Fields in Finite Geometry |c Bernhard Schmidt. |
| 260 | |a Berlin [etc.] : |b Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 1797 |x 1617-9692 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 1. Introduction: The nature of the problems -- The combinatorial structures in question -- Group rings, characters, Fourier analysis -- Number theoretic tools -- Algebraic-combinatorial tools. 2. The field descent: The fixing theorem -- Prescribed absolute value -- Bounding the absoute value -- The modulus equation and the class group. 3. Exponent bounds: Self-conjugacy exponent bounds -- Field descent exponent bounds. 4. Two-weight irreducible cyclic bounds: A necessary and sufficient condition -- All two-weight irreducible cyclic codes?- Partial proof of Conjecture 4.2.4 -- Two-intersection sets and sub-difference sets. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 650 | |a Géométries finies | ||
| 650 | |a Ensembles de différence | ||
| 650 | |a Cyclotomie | ||
| 650 | |a Mathématiques | ||
| 650 | |a Analyse combinatoire | ||
| 776 | 0 | |0 07871544X |t Characters and cyclotomic fields in finite geometry |f Bernhard Schmidt |d 2002 |c Berlin |n Springer |p 1 vol. (VIII-100 p.) |s Lecture notes in mathematics |z 3-540-44243-X | |
| 776 | 0 | |t Characters and Cyclotomic Fields in Finite Geometry |b Texte imprimé |z 9783662183199 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/b84213 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-0RK3MJ5P-7 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:750634774 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.1007/b84213 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:753991020 |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/b84213 |z Accès INSA CVL | |
| 997 | |0 972611 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||