Introduction To Algebraic Coding Theory
DOWNLOAD
Download Introduction To Algebraic Coding Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Introduction To Algebraic Coding Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Introduction To Algebraic Coding Theory
DOWNLOAD
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.
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.
Elements Of Algebraic Coding Theory
DOWNLOAD
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.
An Introduction To Algebraic And Combinatorial Coding Theory
DOWNLOAD
Author : Ian F. Blake
language : en
Publisher: Academic Press
Release Date : 2014-05-10
An Introduction To Algebraic And Combinatorial Coding Theory written by Ian F. Blake and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Elements Of Algebraic Coding Theory
DOWNLOAD
Author : Lekh R. Vermani
language : en
Publisher: Routledge
Release Date : 2022-01-27
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 2022-01-27 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.
Introduction To Coding Theory
DOWNLOAD
Author : J. H. van Lint
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Coding Theory written by J. H. van Lint 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 2013-03-09 with Mathematics categories.
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).
Coding Theory
DOWNLOAD
Author : J. H. van Lint
language : en
Publisher: Springer
Release Date : 2009-08-14
Coding Theory written by J. 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 2009-08-14 with Mathematics categories.
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.
Algebraic Coding Theory Revised Edition
DOWNLOAD
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 Over Finite Commutative Rings
DOWNLOAD
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.
Introduction To Coding Theory And Algebraic Geometry
DOWNLOAD
Author : J. van Lint
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To Coding Theory And Algebraic Geometry written by J. van Lint and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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
Introduction To Coding Theory
DOWNLOAD
Author : Jurgen Bierbrauer
language : en
Publisher: CRC Press
Release Date : 2016-10-14
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 2016-10-14 with Computers categories.
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.