Characters and Cyclotomic Fields in Finite Geometry

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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Bibliographic Details
Main Author: Schmidt, Bernhard (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
Edition:1st ed. 2002.
Series:Lecture Notes in Mathematics, 1797
Subjects:
Combinatorics.
Online Access:Full Text via HEAL-Link
Table of Contents:
  • 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.

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