Mathematics

Algebraic Coding Theory and Information Theory

Algebraic Coding Theory and Information Theory

Author: Alexei Ashikhmin

Publisher: American Mathematical Soc.

ISBN: 0821871102

Category: Mathematics

Page: 177

View: 752

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.
Computers

Algebraic Coding

Algebraic Coding

Author: Gerard Cohen

Publisher: Springer Science & Business Media

ISBN: 3540578439

Category: Computers

Page: 326

View: 978

This book discusses the changes in the regional infrastructure within the European automobile industry. It is based on the increased competition between the European automobile industry and its suppliers, which has several causes: the intensified activities of Japanese competitors in Europe, leading to faster adaptation to new production concepts in European companies (lean production); concentration of suppliers in connection with these new concepts; new opportunities and competition as a result of the home market and the opening of Eastern Europe.
Mathematics

Algebraic Coding Theory (Revised Edition)

Algebraic Coding Theory (Revised Edition)

Author: Elwyn R Berlekamp

Publisher: World Scientific

ISBN: 9789814635912

Category: Mathematics

Page: 500

View: 830

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.
Mathematics

Introduction To Algebraic Coding Theory

Introduction To Algebraic Coding Theory

Author: Tzuong-tsieng Moh

Publisher: World Scientific

ISBN: 9789811220982

Category: Mathematics

Page: 268

View: 599

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.
Mathematics

Elements of Algebraic Coding Theory

Elements of Algebraic Coding Theory

Author: Lekh R. Vermani

Publisher: Routledge

ISBN: 9781351452908

Category: Mathematics

Page: 256

View: 693

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.
Computers

Algebraic Coding Theory and Applications

Algebraic Coding Theory and Applications

Author: Carlos R. P. Hartmann

Publisher: Springer

ISBN: 9783662396414

Category: Computers

Page: 529

View: 534

Mathematics

Algebraic Coding Theory Over Finite Commutative Rings

Algebraic Coding Theory Over Finite Commutative Rings

Author: Steven T. Dougherty

Publisher: Springer

ISBN: 9783319598062

Category: Mathematics

Page: 103

View: 390

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.
Technology & Engineering

A Survey of Algebraic Coding Theory

A Survey of Algebraic Coding Theory

Author: Elwyn R. Berlekamp

Publisher: Springer

ISBN: 9783709143254

Category: Technology & Engineering

Page: 74

View: 906

Coding theory

Algebraic Coding Theory: History and Development

Algebraic Coding Theory: History and Development

Author: Ian F. Blake

Publisher:

ISBN: UOM:39015000489446

Category: Coding theory

Page: 440

View: 507

Mathematics

Introduction to Finite Fields and Their Applications

Introduction to Finite Fields and Their Applications

Author: Rudolf Lidl

Publisher: Cambridge University Press

ISBN: 0521460948

Category: Mathematics

Page: 416

View: 428

Presents an introduction to the theory of finite fields and some of its most important applications.
Mathematics

Handbook of Algebra

Handbook of Algebra

Author:

Publisher: Elsevier

ISBN: 0080532950

Category: Mathematics

Page: 912

View: 663

Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.
Computers

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author: Serdar Boztas

Publisher: Springer Science & Business Media

ISBN: 9783540772231

Category: Computers

Page: 368

View: 145

This book constitutes the refereed proceedings of the 17th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007. The 33 revised full papers presented together with 8 invited papers were carefully reviewed and selected from 61 submissions. Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.