An Introduction To Algebraic And Combinatorial Coding Theory
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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.
An Introduction To Algebraic And Combinatorial Coding Theory
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Author : Olga Moreira
language : en
Publisher:
Release Date : 2023-12
An Introduction To Algebraic And Combinatorial Coding Theory written by Olga Moreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12 with categories.
"An Introduction to Algebraic and Combinatorial Coding Theory" is a comprehensive book that offers a thorough exploration of the principles and techniques of coding theory. It serves as a valuable resource for readers interested in gaining a deeper understanding of error detection and correction in communication systems. With its well-structured chapters covering coding theory fundamentals, algebraic codes, cyclic codes, block codes, and advanced coding techniques, this book caters to the needs of students, researchers, and professionals in the field. It provides a solid foundation in coding theory and showcases its practical applications in various domains, including telecommunications, data storage, and cryptography.
Introduction To Algebraic Coding Theory
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Author : Tzuong-tsieng Moh
language : en
Publisher: World Scientific
Release Date : 2022-02-18
Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Mathematics categories.
In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.
Coding Theory
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Author : Jacobus H. van Lint
language : en
Publisher: Springer
Release Date : 2013-12-11
Coding Theory written by Jacobus H. van Lint and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Twelfth International Workshop On Algebraic And Combinatorial Coding Theory
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Author :
language : en
Publisher:
Release Date : 2010
Twelfth International Workshop On Algebraic And Combinatorial Coding Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebra categories.
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.
Introduction To Coding Theory
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Author : J.H. van Lint
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Coding Theory written by J.H. van Lint 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.
It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction, the chapter requires more mathematical background of the reader than the remainder of this book. One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 7l.4• There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10.
Algebraic Coding Theory Over Finite Commutative Rings
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Author : Steven T. Dougherty
language : en
Publisher: Springer
Release Date : 2017-07-04
Algebraic Coding Theory Over Finite Commutative Rings written by Steven T. Dougherty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-04 with Mathematics categories.
This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.
Introduction To Coding Theory And Algebraic Geometry
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Author : J. van Lint
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To Coding Theory And Algebraic Geometry written by J. van Lint and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
Algebraic Geometric Codes Basic Notions
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Author : Michael Tsfasman
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-15
Algebraic Geometric Codes Basic Notions written by Michael Tsfasman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-15 with Mathematics categories.
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.