Coding Theory And Applications Solved Exercises And Problems Of Linear Codes
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Coding Theory And Applications Solved Exercises And Problems Of Linear Codes
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Author : Enes Pašalić
language : sl
Publisher:
Release Date : 2013
Coding Theory And Applications Solved Exercises And Problems Of Linear Codes written by Enes Pašalić and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Selected Unsolved Problems In Coding Theory
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Author : David Joyner
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-26
Selected Unsolved Problems In Coding Theory written by David Joyner 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 2011-08-26 with Mathematics categories.
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.
Coding Theory
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Author : Sudhakar Radhakrishnan
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-05-25
Coding Theory written by Sudhakar Radhakrishnan and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-25 with Computers categories.
This book explores the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavors. It consists of seven chapters that address such topics as applications of coding theory in networking and cryptography, wireless sensor nodes in wireless body area networks, the construction of linear codes, and more.
Introduction To Coding Theory
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Author : Jurgen Bierbrauer
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Introduction To Coding Theory written by Jurgen Bierbrauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
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
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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.
Computer Algebra In Coding Theory And Cryptanalysis
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Author : Stanislav Bulygin
language : de
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2009-09
Computer Algebra In Coding Theory And Cryptanalysis written by Stanislav Bulygin and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09 with Algebra categories.
This book that represents the author's Ph.D. thesis is devoted to applying symbolic methods to the problems of decoding linear codes and of algebraic cryptanalysis. The initial problems are reformulated in terms of systems of polynomial equations over a finite field, which solution(s) should yield a way to solve the initial problems. Solutions of such systems are obtained using Grobner bases. The first part is devoted to an application of system solving to decoding linear codes. The original method for arbitrary linear codes, which in some sense generalizes the Newton identities method, is proposed. Since for the method to work the field equations" are not needed, it is possible to handle quite large codes. The second part is about the algebraic cryptanalysis of the AES. The systems usually considered in this area have many auxiliary variables that are not needed for the key recovery. Therefore, here the approach is provided where these variables are eliminated and a resulting system in key-variables only is then solved. This is shown to be effective for small scale variants of the AES especially when using several plain-/ciphertext pairs.
Error Correcting Linear Codes
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Author : Anton Betten
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-21
Error Correcting Linear Codes written by Anton Betten 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 2006-09-21 with Mathematics categories.
This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.
Coding Theory
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Author : San Ling
language : en
Publisher: Cambridge University Press
Release Date : 2004-02-12
Coding Theory written by San Ling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-12 with Computers categories.
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.
Coding Theory And Cryptography
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Author : D.C. Hankerson
language : en
Publisher: CRC Press
Release Date : 2000-08-04
Coding Theory And Cryptography written by D.C. Hankerson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-04 with Computers categories.
Containing data on number theory, encryption schemes, and cyclic codes, this highly successful textbook, proven by the authors in a popular two-quarter course, presents coding theory, construction, encoding, and decoding of specific code families in an "easy-to-use" manner appropriate for students with only a basic background in mathematics offering revised and updated material on the Berlekamp-Massey decoding algorithm and convolutional codes. Introducing the mathematics as it is needed and providing exercises with solutions, this edition includes an extensive section on cryptography, designed for an introductory course on the subject.
Algebraic And Stochastic Coding Theory
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Author : Dave K. Kythe
language : en
Publisher: CRC Press
Release Date : 2012-03-05
Algebraic And Stochastic Coding Theory written by Dave K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-05 with Computers categories.
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.