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- catalog abstract "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.".
- catalog contributor b8063087.
- catalog created "c1995.".
- catalog date "1995".
- catalog date "c1995.".
- catalog dateCopyrighted "c1995.".
- catalog description "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.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [169]-179) and index.".
- catalog extent "vi, 181 p. :".
- catalog hasFormat "Finite geometry and character theory.".
- catalog identifier "038759065X (New York : acid-free paper)".
- catalog identifier "354059065X (Berlin : acid-free paper) :".
- catalog isFormatOf "Finite geometry and character theory.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1601.".
- catalog isPartOf "Lecture notes in mathematics ; 1601".
- catalog issued "1995".
- catalog issued "c1995.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Finite geometry and character theory.".
- catalog subject "510 s 514/.223 20".
- catalog subject "510 s 518/.13 20".
- catalog subject "Coding theory.".
- catalog subject "Combinatorics.".
- catalog subject "Difference sets.".
- catalog subject "Finite geometries.".
- catalog subject "Fourier transformations.".
- catalog subject "Geometry.".
- catalog subject "Group theory.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1601 QA167.2".
- catalog tableOfContents "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.".
- catalog title "Finite geometry and character theory / Alexander Pott.".
- catalog type "text".