Characters and Cyclotomic Fields in Finite Geometry: 1797 - Brossura

Schmidt, Bernhard

 
9783540442431: Characters and Cyclotomic Fields in Finite Geometry: 1797
Brossura
ISBN 10: 354044243X ISBN 13: 9783540442431
Casa editrice: Springer, 2009

Sinossi

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.

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Contenuti

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

Product Description

Book by Schmidt Bernhard

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Editore
Springer
Data di pubblicazione
2009
Lingua
Inglese
ISBN 10 
354044243X
ISBN 13 
9783540442431
Rilegatura
Copertina flessibile
Numero di pagine
116
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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