Finite Geometry and Character Theory
Pott, Alexander.
Finite Geometry and Character Theory [electronic resource] / by Alexander Pott. - VIII, 188 p. online resource. - Lecture Notes in Mathematics, 1601 0075-8434 ; . - Lecture Notes in Mathematics, 1601 .
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.
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.
9783540491828
10.1007/BFb0094449 doi
Algebra.
Geometry.
Number theory.
Combinatorics.
Group theory.
Coding theory.
Algebra.
Geometry.
Number Theory.
Combinatorics.
Group Theory and Generalizations.
Coding and Information Theory.
QA150-272
512
Finite Geometry and Character Theory [electronic resource] / by Alexander Pott. - VIII, 188 p. online resource. - Lecture Notes in Mathematics, 1601 0075-8434 ; . - Lecture Notes in Mathematics, 1601 .
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.
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.
9783540491828
10.1007/BFb0094449 doi
Algebra.
Geometry.
Number theory.
Combinatorics.
Group theory.
Coding theory.
Algebra.
Geometry.
Number Theory.
Combinatorics.
Group Theory and Generalizations.
Coding and Information Theory.
QA150-272
512