Finite Geometry and Character Theory

By: Alexander Pott

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Paperback | 6 April 1995

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196 Pages

Dimensions(cm)
24.13 x 15.88 x 1.27

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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 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.

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Preliminaries	p. 1
Basic definitions	p. 1
Algebraic tools	p. 16
Multipliers	p. 27
Examples	p. 35
Difference sets	p. 35
Relative difference sets	p. 40
Divisible difference sets	p. 49
Non-existence results	p. 56
Classical Parameters	p. 69
Singer difference sets	p. 69
The Gordon-Mills-Welch construction	p. 75
The Waterloo problem	p. 95
Semiregular relative difference sets	p. 103
Necessary conditions	p. 104
Examples and characterizations	p. 108
Quasiregular collineation groups	p. 113
Introduction	p. 113
Affine difference sets	p. 115
Direct product difference sets	p. 130
Planar functions	p. 141
Codes and sequences	p. 149
Perfect sequences	p. 149
Almost perfect sequences	p. 153
Abelian difference set codes	p. 157
Bibliography	p. 169
Index	p. 180
Table of Contents provided by Blackwell. All Rights Reserved.

Finite Geometry and Character Theory

At a Glance

Paperback

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