Elements Of Algebraic Coding Theory

Author : L.R. Vermani
Publisher : CRC Press
Page : 270 pages
File Size : 50,5 Mb
Release : 1996-07-01
Category : Mathematics
ISBN : 0412573806

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Elements of Algebraic Coding Theory by L.R. Vermani Pdf

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.

Author : Lekh R. Vermani
Publisher : Routledge
Page : 256 pages
File Size : 41,7 Mb
Release : 2022-01-27
Category : Mathematics
ISBN : 9781351452908

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Elements of Algebraic Coding Theory by Lekh R. Vermani Pdf

Coding theory came into existence in the late 1940s 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.

Author : Tzuong-tsieng Moh
Publisher : World Scientific
Page : 266 pages
File Size : 43,5 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9789811220982

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Introduction To Algebraic Coding Theory by Tzuong-tsieng Moh Pdf

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.

Author : Jacobus H. van Lint
Publisher : Springer
Page : 145 pages
File Size : 49,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662207123

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Coding Theory by Jacobus H. van Lint Pdf

Author : Ian F. Blake
Publisher : Unknown
Page : 440 pages
File Size : 52,9 Mb
Release : 1973
Category : Computers
ISBN : UOM:39015000486285

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Algebraic Coding Theory: History and Development by Ian F. Blake Pdf

Author : Elwyn R Berlekamp
Publisher : World Scientific
Page : 500 pages
File Size : 41,9 Mb
Release : 2015-03-26
Category : Mathematics
ISBN : 9789814635912

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Algebraic Coding Theory (Revised Edition) by Elwyn R Berlekamp Pdf

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 : Jurgen Bierbrauer
Publisher : CRC Press
Page : 512 pages
File Size : 48,7 Mb
Release : 2016-10-14
Category : Computers
ISBN : 9781482299816

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Introduction to Coding Theory by Jurgen Bierbrauer Pdf

This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

Author : J. H. van Lint
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 51,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662079980

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Introduction to Coding Theory by J. H. van Lint Pdf

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 : Harald Niederreiter,Chaoping Xing
Publisher : Princeton University Press
Page : 272 pages
File Size : 41,9 Mb
Release : 2009-09-21
Category : Mathematics
ISBN : 9781400831302

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Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter,Chaoping Xing Pdf

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 : Dave K. Kythe,Prem K. Kythe
Publisher : CRC Press
Page : 507 pages
File Size : 45,5 Mb
Release : 2017-07-28
Category : Computers
ISBN : 9781466505629

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Algebraic and Stochastic Coding Theory by Dave K. Kythe,Prem K. Kythe Pdf

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 : Alexei Ashikhmin,Alexander Barg
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 45,5 Mb
Release : 2024-06-17
Category : Mathematics
ISBN : 0821871102

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Algebraic Coding Theory and Information Theory by Alexei Ashikhmin,Alexander Barg Pdf

Collected here are papers that were presented at or inspired by the DIMACS workshop, Algebraic Coding Theory and Information Theory (Rutgers University, Piscataway, NJ). Among the topics discussed are universal data compression, graph theoretical ideas in the construction of codes and lattices, decoding algorithms, and computation of capacity in various communications schemes. The book is suitable for graduate students and researchers interested in coding and information theory.

Author : J. van Lint,G. van der Geer
Publisher : Birkhäuser
Page : 82 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034892865

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Introduction to Coding Theory and Algebraic Geometry by J. van Lint,G. van der Geer Pdf

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

Author : W. Cary Huffman,Jon-Lark Kim,Patrick Solé
Publisher : CRC Press
Page : 998 pages
File Size : 48,9 Mb
Release : 2021-03-26
Category : Computers
ISBN : 9781351375108

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Concise Encyclopedia of Coding Theory by W. Cary Huffman,Jon-Lark Kim,Patrick Solé Pdf

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

Author : Ian F. Blake,Ronald C. Mullin
Publisher : Academic Press
Page : 242 pages
File Size : 45,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260297

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An Introduction to Algebraic and Combinatorial Coding Theory by Ian F. Blake,Ronald C. Mullin Pdf

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.

Author : David Joyner,Jon-Lark Kim
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 40,8 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9780817682569

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Selected Unsolved Problems in Coding Theory by David Joyner,Jon-Lark Kim Pdf

Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.