Algebra And Coding Theory
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Author |
: Elwyn R Berlekamp |
Publisher |
: World Scientific |
Total Pages |
: 501 |
Release |
: 2015-03-26 |
ISBN-10 |
: 9789814635912 |
ISBN-13 |
: 981463591X |
Rating |
: 4/5 (12 Downloads) |
Synopsis Algebraic Coding Theory (Revised Edition) by : Elwyn R Berlekamp
This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
Author |
: Raymond Hill |
Publisher |
: Oxford University Press |
Total Pages |
: 268 |
Release |
: 1986 |
ISBN-10 |
: 0198538030 |
ISBN-13 |
: 9780198538035 |
Rating |
: 4/5 (30 Downloads) |
Synopsis A First Course in Coding Theory by : Raymond Hill
Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.
Author |
: Harald Niederreiter |
Publisher |
: Princeton University Press |
Total Pages |
: 272 |
Release |
: 2009-09-21 |
ISBN-10 |
: 9781400831302 |
ISBN-13 |
: 140083130X |
Rating |
: 4/5 (02 Downloads) |
Synopsis Algebraic Geometry in Coding Theory and Cryptography by : Harald Niederreiter
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
Author |
: Steven T. Dougherty |
Publisher |
: Springer |
Total Pages |
: 109 |
Release |
: 2017-07-04 |
ISBN-10 |
: 9783319598062 |
ISBN-13 |
: 3319598066 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Algebraic Coding Theory Over Finite Commutative Rings by : Steven T. Dougherty
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.
Author |
: Everett W. Howe |
Publisher |
: Springer |
Total Pages |
: 160 |
Release |
: 2017-11-15 |
ISBN-10 |
: 9783319639314 |
ISBN-13 |
: 3319639315 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Algebraic Geometry for Coding Theory and Cryptography by : Everett W. Howe
Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.
Author |
: Dave K. Kythe |
Publisher |
: CRC Press |
Total Pages |
: 507 |
Release |
: 2017-07-28 |
ISBN-10 |
: 9781466505629 |
ISBN-13 |
: 1466505621 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Algebraic and Stochastic Coding Theory by : Dave K. Kythe
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.
Author |
: Jacobus H. van Lint |
Publisher |
: Springer |
Total Pages |
: 145 |
Release |
: 2013-12-11 |
ISBN-10 |
: 9783662207123 |
ISBN-13 |
: 3662207125 |
Rating |
: 4/5 (23 Downloads) |
Synopsis Coding Theory by : Jacobus H. van Lint
Author |
: J. H. van Lint |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 181 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9783662079980 |
ISBN-13 |
: 3662079984 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Introduction to Coding Theory by : J. H. van Lint
Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathe maticians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. So, it is not surprising that one more book on this subject now appears. However, a little more justification of the book are necessary. A few years ago it was and a little more history remarked at a meeting on coding theory that there was no book available an introductory course on coding theory (mainly which could be used for for mathematicians but also for students in engineering or computer science). The best known textbooks were either too old, too big, too technical, too much for specialists, etc. The final remark was that my Springer Lecture Notes (# 201) were slightly obsolete and out of print. Without realizing what I was getting into I announced that the statement was not true and proved this by showing several participants the book Inleiding in de Coderingstheorie, a little book based on the syllabus of a course given at the Mathematical Centre in Amsterdam in 1975 (M. C. Syllabus 31).
Author |
: Ian F. Blake |
Publisher |
: Academic Press |
Total Pages |
: 369 |
Release |
: 2014-05-10 |
ISBN-10 |
: 9781483260594 |
ISBN-13 |
: 1483260593 |
Rating |
: 4/5 (94 Downloads) |
Synopsis The Mathematical Theory of Coding by : Ian F. Blake
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.
Author |
: L.R. Vermani |
Publisher |
: CRC Press |
Total Pages |
: 270 |
Release |
: 1996-07-01 |
ISBN-10 |
: 0412573806 |
ISBN-13 |
: 9780412573804 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Elements of Algebraic Coding Theory by : L.R. Vermani
Coding theory came into existence in the late 1940's and is concerned with devising efficient encoding and decoding procedures. The book is intended as a principal text for first courses in coding and algebraic coding theory, and is aimed at advanced undergraduates and recent graduates as both a course and self-study text. BCH and cyclic, Group codes, Hamming codes, polynomial as well as many other codes are introduced in this textbook. Incorporating numerous worked examples and complete logical proofs, it is an ideal introduction to the fundamental of algebraic coding.