Algebraic Coding
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Algebraic Coding Theory Revised Edition
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Author : Elwyn R Berlekamp
language : en
Publisher: World Scientific
Release Date : 2015-03-26
Algebraic Coding Theory Revised Edition written by Elwyn R Berlekamp and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-26 with Mathematics categories.
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.
Algebraic Coding Theory And Applications
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Author : Carlos R. P. Hartmann
language : en
Publisher: Springer
Release Date : 2013-12-19
Algebraic Coding Theory And Applications written by Carlos R. P. Hartmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Computers categories.
Algebraic Coding Theory History And Development
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Author : Ian F. Blake
language : en
Publisher:
Release Date : 1973
Algebraic Coding Theory History And Development written by Ian F. Blake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Computers categories.
Elements Of Algebraic Coding Theory
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Author : L.R. Vermani
language : en
Publisher: CRC Press
Release Date : 2022-01-26
Elements Of Algebraic Coding Theory written by L.R. Vermani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-26 with Mathematics categories.
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.
Elements Of Algebraic Coding Theory
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Author : L.R. Vermani
language : en
Publisher: CRC Press
Release Date : 1996-07-01
Elements Of Algebraic Coding Theory written by L.R. Vermani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-01 with Mathematics categories.
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 Algebraic Coding Theory
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Author : Tzuong-tsieng Moh
language : en
Publisher: World Scientific
Release Date : 2022-02-18
Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Mathematics categories.
We live in the age of technology where messages are transmitted in sequences of 0's and 1's through space. It is possible to make an error with noisy channels, so self-correcting codes become vital to eradicate all errors (as the number of errors is small). These self-correcting codes are widely used in the industry for a variety of applications including e-mail, telephone, remote sensing (e.g., photographs of Mars), amongst others.We will present some essentials of the theory in this book. Using linear algebra, we have the salient Hamming codes. The next level of coding theory is through the usage of ring theory, especially polynomials, rational functions and power series, to produce BCH codes, Reed-Solomon codes and the classical Goppa codes. Then we progress to the geometric Goppa code using Algebraic Geometry.
Algebraic Coding Theory And Information Theory
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Author : Alexei Ashikhmin
language : en
Publisher: American Mathematical Soc.
Release Date :
Algebraic Coding Theory And Information Theory written by Alexei Ashikhmin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Elements Of Algebraic Coding Theory
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Author : Lekh R. Vermani
language : en
Publisher: Routledge
Release Date : 2022-01-26
Elements Of Algebraic Coding Theory written by Lekh R. Vermani and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-26 with Mathematics categories.
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.
Algebraic Coding Theory Over Finite Commutative Rings
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Author : Steven T. Dougherty
language : en
Publisher: Springer
Release Date : 2017-07-04
Algebraic Coding Theory Over Finite Commutative Rings written by Steven T. Dougherty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-04 with Mathematics categories.
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.
Algebraic Coding Theory
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Author : Elwyn R. Berlekamp
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015
Algebraic Coding Theory written by Elwyn R. Berlekamp and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Computers categories.
In 1948, Claude Shannon showed the existence of codes which could correct errors. Over the next two decades, he and others explored the theoretical limits of the performance of long block codes, resulting in curves such as the one shown above. In the 1960s, mathematicians introduced the notion that the sophisticated algebra of finite fields might be used to design and implement such codes. When the first edition of this book appeared in 1968, it immediately became a landmark in the field. It introduced a novel algorithm for factoring polynomials, the crux of which is the top formula on the left of the cover. It also introduced a new algorithm for determining the polynomial that needs to be factored in order to decode Reed-Solomon codes. The crux of this algorithm, which appears on the bottom left of the cover, became widely known as the Berlekamp-Massey algorithm. These advances made algebraic error-correcting codes feasible for a wide range of applications in both computer memories and in digital communications. Building on the foundations of this book a subsequent breakthrough in the 1970s reduced the complexity of nonbinary Reed-Solomon encoders to that of much simpler binary codes of comparable redundancies. A circuit diagram for such an encoder appears on the right of the cover. It became a NASA standard for deep space communications.