Characters and Cyclotomic Fields in Finite Geometry

• Κύριος συγγραφέας: Schmidt, Bernhard (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Έκδοση: 1st ed. 2002.
• Σειρά: Lecture Notes in Mathematics, 1797
• Θέματα: Combinatorics.

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...

Πίνακας περιεχομένων:

• 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.