Different Aspects Of Coding Theory

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Different Aspects of Coding Theory

Robert Calderbank
Different Aspects of Coding Theory Book PDF

Author : Robert Calderbank
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 48,6 Mb
Release : 1995
Category : Automate
ISBN : 9780821803790

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Different Aspects of Coding Theory by Robert Calderbank Pdf

The symposia in applied mathematics have been held under the auspices of the American Mathematical Society and others since 1967. This books connects coding theory with actual applications in consumer electronics and with other areas of mathematics. It covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science.

Coding Theory

J. H. van Lint
Coding Theory Book PDF

Author : J. H. van Lint
Publisher : Springer
Page : 146 pages
File Size : 52,8 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9783540366577

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Coding Theory by J. H. van Lint Pdf

These lecture notes are the contents of a two-term course given by me during the 1970-1971 academic year as Morgan Ward visiting professor at the California Institute of Technology. The students who took the course were mathematics seniors and graduate students. Therefore a thorough knowledge of algebra. (a. o. linear algebra, theory of finite fields, characters of abelian groups) and also probability theory were assumed. After introducing coding theory and linear codes these notes concern topics mostly from algebraic coding theory. The practical side of the subject, e. g. circuitry, is not included. Some topics which one would like to include 1n a course for students of mathematics such as bounds on the information rate of codes and many connections between combinatorial mathematics and coding theory could not be treated due to lack of time. For an extension of the course into a third term these two topics would have been chosen. Although the material for this course came from many sources there are three which contributed heavily and which were used as suggested reading material for the students. These are W. W. Peterson's Error-Correcting Codes «(15]), E. R. Berlekamp's Algebraic Coding Theory «(5]) and several of the AFCRL-reports by E. F. Assmus, H. F. Mattson and R. Turyn ([2], (3), [4] a. o. ). For several fruitful discussions I would like to thank R. J. McEliece.

Concise Encyclopedia of Coding Theory

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

Author : W. Cary Huffman,Jon-Lark Kim,Patrick Solé
Publisher : CRC Press
Page : 998 pages
File Size : 52,6 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

Elements of Algebraic Coding Theory

Lekh R. Vermani
Elements of Algebraic Coding Theory Book PDF

Author : Lekh R. Vermani
Publisher : Routledge
Page : 256 pages
File Size : 52,9 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.

Introduction to Coding Theory

Jurgen Bierbrauer
Introduction to Coding Theory Book PDF

Author : Jurgen Bierbrauer
Publisher : CRC Press
Page : 267 pages
File Size : 55,5 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781351989602

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Introduction to Coding Theory by Jurgen Bierbrauer Pdf

Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.

Coding Theory, Cryptography and Related Areas

Johannes Buchmann,Tom Hoeholdt,Henning Stichtenoth,Horacio Tapia-Recillas
Coding Theory Cryptography and Related Areas Book PDF

Author : Johannes Buchmann,Tom Hoeholdt,Henning Stichtenoth,Horacio Tapia-Recillas
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642571893

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Coding Theory, Cryptography and Related Areas by Johannes Buchmann,Tom Hoeholdt,Henning Stichtenoth,Horacio Tapia-Recillas Pdf

A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.

Elements of Algebraic Coding Theory

L.R. Vermani
Elements of Algebraic Coding Theory Book PDF

Author : L.R. Vermani
Publisher : CRC Press
Page : 270 pages
File Size : 45,7 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.

Introduction to Coding Theory

Ron Roth
Introduction to Coding Theory Book PDF

Author : Ron Roth
Publisher : Cambridge University Press
Page : 592 pages
File Size : 49,5 Mb
Release : 2006-02-23
Category : Computers
ISBN : 0521845041

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Introduction to Coding Theory by Ron Roth Pdf

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Algebraic Geometry in Coding Theory and Cryptography

Harald Niederreiter,Chaoping Xing
Algebraic Geometry in Coding Theory and Cryptography Book PDF

Author : Harald Niederreiter,Chaoping Xing
Publisher : Princeton University Press
Page : 272 pages
File Size : 53,7 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

Coding Theory

Andre Neubauer,Jurgen Freudenberger,Volker Kuhn
Coding Theory Book PDF

Author : Andre Neubauer,Jurgen Freudenberger,Volker Kuhn
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 54,6 Mb
Release : 2007-10-22
Category : Technology & Engineering
ISBN : 0470519827

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Coding Theory by Andre Neubauer,Jurgen Freudenberger,Volker Kuhn Pdf

One of the most important key technologies for digital communication systems as well as storage media is coding theory. It provides a means to transmit information across time and space over noisy and unreliable communication channels. Coding Theory: Algorithms, Architectures and Applications provides a concise overview of channel coding theory and practice, as well as the accompanying signal processing architectures. The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low density parity check codes and space-time codes. Coding Theory provides algorithms and architectures used for implementing coding and decoding strategies as well as coding schemes used in practice especially in communication systems. Feature of the book include: Unique presentation-like style for summarising main aspects Practical issues for implementation of coding techniques Sound theoretical approach to practical, relevant coding methodologies Covers standard coding schemes such as block and convolutional codes, coding schemes such as Turbo and LDPC codes, and space time codes currently in research, all covered in a common framework with respect to their applications. This book is ideal for postgraduate and undergraduate students of communication and information engineering, as well as computer science students. It will also be of use to engineers working in the industry who want to know more about the theoretical basics of coding theory and their application in currently relevant communication systems

Coding Theory

Sudhakar Radhakrishnan,Muhammad Sarfraz
Coding Theory Book PDF

Author : Sudhakar Radhakrishnan,Muhammad Sarfraz
Publisher : BoD – Books on Demand
Page : 228 pages
File Size : 47,8 Mb
Release : 2020-03-11
Category : Computers
ISBN : 9781789844429

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Coding Theory by Sudhakar Radhakrishnan,Muhammad Sarfraz Pdf

This book is intended to attract the attention of practitioners and researchers in academia and industry interested in challenging paradigms of coding theory and computer vision. The chapters in this comprehensive reference explore the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavours. This book is compiled with a view to provide researchers, academicians, and readers with an in-depth discussion of the latest advances in this field. It consists of twelve chapters from academicians, practitioners, and researchers from different disciplines of life. All the chapters are authored by various researchers around the world covering the field of coding theory and image and video processing. This book mainly focusses on researchers who can do quality research in the area of coding theory and image and video processing and related fields. Each chapter is an independent research study, which will motivate young researchers to think about. These twelve chapters are presented in three sections and will be an eye-opener for all who systematic researchers in these fields.

Selected Topics in Information and Coding Theory

Isaac Woungang
Selected Topics in Information and Coding Theory Book PDF

Author : Isaac Woungang
Publisher : World Scientific
Page : 725 pages
File Size : 48,6 Mb
Release : 2010
Category : Computers
ISBN : 9789812837172

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Selected Topics in Information and Coding Theory by Isaac Woungang Pdf

Pt. 1. Applications of coding theory to computational complexity. ch. 1. Linear complexity and related complexity measures / Arne Winterhof. ch. 2. Lattice and construction of high coding gain lattices from codes / Mohammd-Reza Sadeghi. ch. 3. Distributed space-time codes with low ML decoding complexity / G. Susinder Rajan and B. Sundar Rajan -- pt. 2. Methods of algebraic combinatorics in coding theory/codes construction and existence. ch. 4. Coding theory and algebraic combinatorics / Michael Huber. ch. 5. Block codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 6. LDPC and convolutional codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 7. Search for good linear codes in the class of quasi-cyclic and related codes / Nuh Aydin and Tsvetan Asamov -- pt. 3. Source coding/channel capacity/network coding. ch. 8. Applications of universal source coding to statistical analysis of time series / Boris Ryabko. ch. 9. Introduction to network coding for acyclic and cyclic networks / Ángela I. Barbero and Øyvind Ytrehus. ch. 10. Distributed joint source-channel coding on a multiple access channel / Vinod Sharma and R. Rajesh -- pt. 4. Other selected topics in information and coding theory. ch. 11. Low-density parity-check codes and the related performance analysis methods / Xudong Ma. ch. 12. Variable length codes and finite automata / Marie-Pierre Béal [und weitere]. ch. 13. Decoding and finding the minimum distance with Gröbner Bases : history and new insights / Stanislav Bulygin and Ruud Pellikaan. ch. 14. Cooperative diversity systems for wireless communication / Murat Uysal and Muhammad Mehboob Fareed. ch. 15. Public key cryptography and coding theory / Pascal Véron

Coding Theory and Quantum Computing

David Evans
Coding Theory and Quantum Computing Book PDF

Author : David Evans
Publisher : American Mathematical Soc.
Page : 166 pages
File Size : 41,9 Mb
Release : 2005
Category : Coding theory
ISBN : 9780821836002

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Coding Theory and Quantum Computing by David Evans Pdf

A conference, Coding Theory and Quantum Computing, was held in Charlottesville, VA, to provide an opportunity for computer scientists, mathematicians, and physicists to interact about subjects of common interest. This proceedings volume grew out of that meeting. It is divided into two parts: "Coding Theory" and "Quantum Computing". In the first part, Harold Ward gives an introduction to coding theory. Other papers survey recent important work, such as coding theory applications of Grobner bases, methods of computing parameters of codes corresponding to algebraic curves, and problems in the theory of designs. The second part of the book covers a wide variety of directions in quantum information with an emphasis on understanding entanglement. The material presented is suitable for graduate students and researchers interested in coding theory and in quantum computing.

Topics in Geometry, Coding Theory and Cryptography

Arnaldo Garcia,Henning Stichtenoth
Topics in Geometry Coding Theory and Cryptography Book PDF

Author : Arnaldo Garcia,Henning Stichtenoth
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 47,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9781402053344

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Topics in Geometry, Coding Theory and Cryptography by Arnaldo Garcia,Henning Stichtenoth Pdf

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

Coding Theory

San Ling,Chaoping Xing
Coding Theory Book PDF

Author : San Ling,Chaoping Xing
Publisher : Cambridge University Press
Page : 238 pages
File Size : 42,7 Mb
Release : 2004-02-12
Category : Computers
ISBN : 0521529239

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Coding Theory by San Ling,Chaoping Xing Pdf

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.