Characters and Cyclotomic Fields in Finite Geometry
Edition: 1 edition
Publisher: Springer
Published: December 5, 2002
Language: eng
Format: Paperback
Number of pages: 100
ISBN-13: 9783540442431
Subjects: Finite geometry; Science/Mathematics; Finite geometries; Algebraic Fields; Combinatorial Geometry; Mathematics; Group Theory; General; Discrete Mathematics; Geometry - General; Barker sequences; Circulant Hadamard matrices; Differences sets; Mathematics / Combinatorics; irreducible cyclic codes; Combinatorics; Cyclotomy; Difference sets
First sentence: This monograph contributes to the existence theory of combinatorial objects admitting certain types of automorphism groups.
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.