A Course In Algebraic Error Correcting Codes

Author : Simeon Ball
Publisher : Springer Nature
Page : 185 pages
File Size : 55,7 Mb
Release : 2020-05-08
Category : Mathematics
ISBN : 9783030411534

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A Course in Algebraic Error-Correcting Codes by Simeon Ball Pdf

This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

Author : Simeon Michael Ball
Publisher : Unknown
Page : 0 pages
File Size : 55,5 Mb
Release : 2020
Category : Coding theory
ISBN : 3030411540

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A Course in Algebraic Error-Correcting Codes by Simeon Michael Ball Pdf

This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon's theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

Author : D J. Baylis
Publisher : Routledge
Page : 113 pages
File Size : 46,8 Mb
Release : 2018-05-11
Category : Mathematics
ISBN : 9781351449830

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Error Correcting Codes by D J. Baylis Pdf

Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style.Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.

Author : Jørn Justesen,Tom Høholdt
Publisher : European Mathematical Society
Page : 210 pages
File Size : 50,9 Mb
Release : 2004
Category : Error-correcting codes (Information theory)
ISBN : 3037190019

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A Course in Error-correcting Codes by Jørn Justesen,Tom Høholdt Pdf

This book is written as a text for a course aimed at advanced undergraduates. Chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts.

Author : J. H. van Lint
Publisher : Springer
Page : 146 pages
File Size : 48,5 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.

Author : Raymond Hill
Publisher : Oxford University Press
Page : 268 pages
File Size : 50,5 Mb
Release : 1986
Category : Computers
ISBN : 0198538030

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A First Course in Coding Theory by Raymond Hill Pdf

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 : Oliver Pretzel
Publisher : Oxford University Press, USA
Page : 424 pages
File Size : 43,6 Mb
Release : 1992
Category : Computers
ISBN : STANFORD:36105000110978

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Error-correcting Codes and Finite Fields by Oliver Pretzel Pdf

Starting with the elementary ideas of parity check codes, this work takes the reader via BCH and Reed-Solomon codes all the way to the geometric Goppa codes. The necessary mathematics is developed in parallel with the applications.

Author : Vera Pless
Publisher : John Wiley & Sons
Page : 198 pages
File Size : 43,7 Mb
Release : 1982
Category : Error-correcting codes (Information theory).
ISBN : MINN:31951D00163539M

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Introduction to the Theory of Error-correcting Codes by Vera Pless Pdf

Introduction to the Theory of Error-Correcting Codes, Third Edition is the ideal textbook for senior-undergraduate and first-year graduate courses on error-correcting codes in mathematics, computer science, and electrical engineering.

Author : Florence Jessie MacWilliams,Neil James Alexander Sloane
Publisher : Elsevier
Page : 787 pages
File Size : 43,7 Mb
Release : 1977
Category : Computers
ISBN : 9780444850102

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The Theory of Error-correcting Codes by Florence Jessie MacWilliams,Neil James Alexander Sloane Pdf

Author : John Baylis
Publisher : Unknown
Page : 219 pages
File Size : 46,9 Mb
Release : 2003
Category : Error-correcting codes (Information theory)
ISBN : OCLC:56937943

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Error-correcting Codes by John Baylis Pdf

Author : David Joyner,Jon-Lark Kim
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 46,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9780817682569

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Selected Unsolved Problems in Coding Theory by David Joyner,Jon-Lark Kim Pdf

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.

Author : Thomas Beth,Michael Clausen
Publisher : Unknown
Page : 228 pages
File Size : 50,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662207796

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Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra by Thomas Beth,Michael Clausen Pdf

Author : Shu Lin,Juane Li
Publisher : Cambridge University Press
Page : 843 pages
File Size : 54,9 Mb
Release : 2021-12-09
Category : Computers
ISBN : 9781316512623

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Fundamentals of Classical and Modern Error-Correcting Codes by Shu Lin,Juane Li Pdf

An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.

Author : Wolfgang Ebeling
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 54,7 Mb
Release : 2013
Category : Computers
ISBN : 9783658003593

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Lattices and Codes by Wolfgang Ebeling Pdf

The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated. Content Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes. Readership Graduate Students in Mathematics and Computer Science Mathematicians and Computer Scientists About the Author Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany

Author : G. Cohen
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0387601147

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Applied Algebra, Algebraic Algorithms And Error-correcting Codes by G. Cohen Pdf