Codes From Difference Sets
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Codes From Difference Sets
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Author : Cunsheng Ding
language : en
Publisher: World Scientific
Release Date : 2014-08-08
Codes From Difference Sets written by Cunsheng Ding and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-08 with Mathematics categories.
This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.
Difference Sets
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Author : Emily H. Moore
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-13
Difference Sets written by Emily H. Moore and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Mathematics categories.
Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of f
Difference Sets Sequences And Their Correlation Properties
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Author : A. Pott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Difference Sets Sequences And Their Correlation Properties written by A. Pott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The explanation of the formal duality of Kerdock and Preparata codes is one of the outstanding results in the field of applied algebra in the last few years. This result is related to the discovery of large sets of quad riphase sequences over Z4 whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups. It is the purpose of this book to illustrate the connection between these three topics. Most articles grew out of lectures given at the NATO Ad vanced Study Institute on "Difference sets, sequences and their correlation properties". This workshop took place in Bad Windsheim (Germany) in August 1998. The editors thank the NATO Scientific Affairs Division for the generous support of this workshop. Without this support, the present collection of articles would not have been realized.
Finite Geometry And Character Theory
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Author : Alexander Pott
language : en
Publisher: Springer
Release Date : 2006-11-14
Finite Geometry And Character Theory written by Alexander Pott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Contemporary Design Theory
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Author : Jeffrey H. Dinitz
language : en
Publisher: John Wiley & Sons
Release Date : 1992-08-04
Contemporary Design Theory written by Jeffrey H. Dinitz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-04 with Mathematics categories.
Foremost experts in their field have contributed articles resulting in a compilation of useful and timely surveys in this ever-expanding field. Each of these 12 original papers covers important aspects of design theory including several in areas that have not previously been surveyed. Also contains surveys updating earlier ones where research is particularly active.
Concise Encyclopedia Of Coding Theory
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Author : W. Cary Huffman
language : en
Publisher: CRC Press
Release Date : 2021-03-25
Concise Encyclopedia Of Coding Theory written by W. Cary Huffman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Computers categories.
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
Designs And Their Codes
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Author : E. F. Assmus
language : en
Publisher: Cambridge University Press
Release Date : 1994-01-06
Designs And Their Codes written by E. F. Assmus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-06 with Mathematics categories.
A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
Combinatorial Designs And Their Applications
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Author : Kathleen Quinn
language : en
Publisher: CRC Press
Release Date : 1999-01-29
Combinatorial Designs And Their Applications written by Kathleen Quinn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-29 with Mathematics categories.
The fruit of a conference that gathered seven very active researchers in the field, Combinatorial Design and their Applications presents a wide but representative range of topics on the non-geometrical aspects of design theory. By concentrating on a few important areas, the authors succeed in providing greater detail in these areas in a more complete and accessible form. Through their contributions to this collection, they help fill a gap in the available combinatorics literature. The papers included in this volume cover recent developments in areas of current interest, such as difference sets, cryptography, and optimal linear codes. Researchers in combinatorics and other areas of pure mathematics, along with researchers in statistics and computer design will find in-depth, up-to-date discussions of design theory and the application of the theory to statistical design, codes, and cryptography.
An Introduction To Algebraic And Combinatorial Coding Theory
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Author : Ian F. Blake
language : en
Publisher: Academic Press
Release Date : 2014-05-10
An Introduction To Algebraic And Combinatorial Coding Theory written by Ian F. Blake and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
An Introduction to Algebraic and Combinatorial Coding Theory focuses on the principles, operations, and approaches involved in the combinatorial coding theory, including linear transformations, chain groups, vector spaces, and combinatorial constructions. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on quadratic residues and codes, self-dual and quasicyclic codes, balanced incomplete block designs and codes, polynomial approach to coding, and linear transformations of vector spaces over finite fields. The text then examines coding and combinatorics, including chains and chain groups, equidistant codes, matroids, graphs, and coding, matroids, and dual chain groups. The manuscript also ponders on Möbius inversion formula, Lucas's theorem, and Mathieu groups. The publication is a valuable source of information for mathematicians and researchers interested in the combinatorial coding theory.
The Mathematical Theory Of Coding
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Author : Ian F. Blake
language : en
Publisher: Academic Press
Release Date : 2014-05-10
The Mathematical Theory Of Coding written by Ian F. Blake and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.