Characters and Cyclotomic Fields in Finite Geometry

Bernhard Schmidt

Characters and Cyclotomic Fields in Finite Geometry
Format
Paperback
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Country
Germany
Published
23 October 2002
Pages
108
ISBN
9783540442431

Characters and Cyclotomic Fields in Finite Geometry

Bernhard Schmidt

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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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