Mathematics
Algebraic Coding Theory and Information Theory
Author: Alexei Ashikhmin
Publisher: American Mathematical Soc.
ISBN: 0821871102
Category: Mathematics
Page: 200
View: 761
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
Author: Gerard Cohen
Publisher: Springer Science & Business Media
ISBN: 3540551301
Category: Computers
Page: 178
View: 232
This volume presents the proceedings of the first French-Soviet workshop on algebraic coding, held in Paris in July 1991. The idea for the workshop, born in Leningrad (now St. Petersburg) in 1990, was to bring together some of the best Soviet coding theorists. Scientists from France, Finland, Germany, Israel, Italy, Spain, and the United States also attended. The papers in the volume fall rather naturally into four categories: - Applications of exponential sums - Covering radius - Constructions -Decoding.
Mathematics
Algebraic Coding Theory (Revised Edition)
Author: Elwyn R Berlekamp
Publisher: World Scientific
ISBN: 9789814635912
Category: Mathematics
Page: 500
View: 373
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
Author: Tzuong-tsieng Moh
Publisher: World Scientific
ISBN: 9789811220982
Category: Mathematics
Page: 268
View: 863
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
Author: Lekh R. Vermani
Publisher: Routledge
ISBN: 9781351452908
Category: Mathematics
Page: 256
View: 501
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
Author: Carlos R. P. Hartmann
Publisher: Springer
ISBN: 9783662396414
Category: Computers
Page: 529
View: 269
Mathematics
Algebraic Coding Theory Over Finite Commutative Rings
Author: Steven T. Dougherty
Publisher: Springer
ISBN: 9783319598062
Category: Mathematics
Page: 103
View: 768
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
Author: Elwyn R. Berlekamp
Publisher: Springer
ISBN: 9783709143254
Category: Technology & Engineering
Page: 74
View: 899
Coding theory
Algebraic Coding Theory: History and Development
Author: Ian F. Blake
Publisher:
ISBN: UOM:39015000489446
Category: Coding theory
Page: 440
View: 797
Mathematics
Introduction to Finite Fields and Their Applications
Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 0521460948
Category: Mathematics
Page: 446
View: 906
Presents an introduction to the theory of finite fields and some of its most important applications.
Mathematics
Handbook of Algebra
Author:
Publisher: Elsevier
ISBN: 0080532950
Category: Mathematics
Page: 912
View: 233
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
Author: Serdar Boztas
Publisher: Springer Science & Business Media
ISBN: 9783540772231
Category: Computers
Page: 379
View: 163
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.