Introduction To Algebraic Coding Theory

Author : Tzuong-tsieng Moh
Publisher : World Scientific
ISBN 13 : 9811220980
Total Pages : 266 pages
Book Rating : 4.82/5 ( download)

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Download or read book Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and published by World Scientific. This book was released on 2022-02-18 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Elwyn R Berlekamp
Publisher : World Scientific
ISBN 13 : 981463591X
Total Pages : 501 pages
Book Rating : 4.12/5 ( download)

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Download or read book Algebraic Coding Theory (Revised Edition) written by Elwyn R Berlekamp and published by World Scientific. This book was released on 2015-03-26 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J.H. van Lint
Publisher : Springer Science & Business Media
ISBN 13 : 3642585752
Total Pages : 244 pages
Book Rating : 4.53/5 ( download)

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Download or read book Introduction to Coding Theory written by J.H. van Lint and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Raymond Hill
Publisher : Oxford University Press
ISBN 13 : 9780198538035
Total Pages : 268 pages
Book Rating : 4.30/5 ( download)

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Download or read book A First Course in Coding Theory written by Raymond Hill and published by Oxford University Press. This book was released on 1986 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J. H. van Lint
Publisher : Springer Science & Business Media
ISBN 13 : 3662079984
Total Pages : 181 pages
Book Rating : 4.80/5 ( download)

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Download or read book Introduction to Coding Theory written by J. H. van Lint and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Lekh R. Vermani
Publisher : Routledge
ISBN 13 : 1351452908
Total Pages : 256 pages
Book Rating : 4.08/5 ( download)

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Download or read book Elements of Algebraic Coding Theory written by Lekh R. Vermani and published by Routledge. This book was released on 2022-01-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Steven T. Dougherty
Publisher : Springer
ISBN 13 : 3319598066
Total Pages : 103 pages
Book Rating : 4.62/5 ( download)

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Download or read book Algebraic Coding Theory Over Finite Commutative Rings written by Steven T. Dougherty and published by Springer. This book was released on 2017-07-04 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ian F. Blake
Publisher : Academic Press
ISBN 13 : 1483260291
Total Pages : 244 pages
Book Rating : 4.97/5 ( download)

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Download or read book An Introduction to Algebraic and Combinatorial Coding Theory written by Ian F. Blake and published by Academic Press. This book was released on 2014-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Juergen Bierbrauer
Publisher : Chapman & Hall/CRC
ISBN 13 : 9781482299809
Total Pages : 0 pages
Book Rating : 4.01/5 ( download)

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Download or read book Introduction to Coding Theory written by Juergen Bierbrauer and published by Chapman & Hall/CRC. This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Harald Niederreiter
Publisher : Princeton University Press
ISBN 13 : 140083130X
Total Pages : 272 pages
Book Rating : 4.02/5 ( download)

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Download or read book Algebraic Geometry in Coding Theory and Cryptography written by Harald Niederreiter and published by Princeton University Press. This book was released on 2009-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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