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Finite geometry and character theory /

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Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described usi...

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Bibliographic Details
Main Author: Pott, Alexander, 1961-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [1995]
Series:Lecture notes in mathematics (Springer-Verlag) ; 1601.
Subjects:
Finite geometries.
Difference sets.
Fourier transformations.
Géométries finies.
Ensembles de différence.
Fourier, Transformations de.
Eindige meetkunde.
Charakter (Gruppentheorie)
Endliche Geometrie.
Algebraische Zahlentheorie.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. Preliminaries. 1.1. Basic definitions. 1.2. Algebraic tools. 1.3. Multipliers
  • 2. Examples. 2.1. Difference sets. 2.2. Relative difference sets. 2.3. Divisible difference sets. 2.4. Non-existence results
  • 3. Classical Parameters. 3.1. Singer difference sets. 3.2. The Gordon-Mills-Welch construction. 3.3. The Waterloo problem
  • 4. Semiregular relative difference sets. 4.1. Necessary conditions. 4.2. Examples and characterizations
  • 5. Quasiregular collineation groups
  • 5.1. Introduction. 5.2. Affine difference sets. 5.3. Direct product difference sets. 5.4. Planar functions
  • 6. Codes and sequences. 6.1. Perfect sequences. 6.2. Almost perfect sequences. 6.3. Abelian difference set codes.