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 using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.

Bibliographic Information

Book Title: Finite Geometry and Character Theory
Authors: Alexander Pott
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0094449
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1995
Softcover ISBN: 978-3-540-59065-1Published: 06 April 1995
eBook ISBN: 978-3-540-49182-8Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 188
Topics: Algebra, Geometry, Number Theory, Combinatorics, Group Theory and Generalizations, Coding and Information Theory

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Finite Geometry and Character Theory

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Table of contents (6 chapters)

Front Matter

Preliminaries: Incidence structures with singer groups

Examples: Existence and non-existence

Difference sets with classical parameters

Semiregular relative difference sets

Projective planes with quasiregular collineation groups

Codes and sequences

Back Matter

Keywords

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