An Introduction To Algebraic And Combinatorial Coding Theory
Download An Introduction To Algebraic And Combinatorial Coding Theory full books in PDF, epub, and Kindle. Read online free An Introduction To Algebraic And Combinatorial Coding Theory ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Ian F. Blake |
Publisher | : Academic Press |
Total Pages | : 244 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483260291 |
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.
Author | : Jacobus H. van Lint |
Publisher | : Springer |
Total Pages | : 145 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 3662207125 |
Author | : Ian F. Blake |
Publisher | : Academic Press |
Total Pages | : 369 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483260593 |
The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.
Author | : Simeon Ball |
Publisher | : Springer Nature |
Total Pages | : 185 |
Release | : 2020-05-08 |
Genre | : Mathematics |
ISBN | : 3030411532 |
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 | : Scott A. Vanstone |
Publisher | : Springer Science & Business Media |
Total Pages | : 297 |
Release | : 2013-04-18 |
Genre | : Technology & Engineering |
ISBN | : 1475720327 |
5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.
Author | : Raymond Hill |
Publisher | : Oxford University Press |
Total Pages | : 268 |
Release | : 1986 |
Genre | : Computers |
ISBN | : 9780198538035 |
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 | : Judy L. Walker |
Publisher | : American Mathematical Soc. |
Total Pages | : 82 |
Release | : 2000 |
Genre | : Computers |
ISBN | : 082182628X |
Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above it discussed."--BOOK JACKET.
Author | : Harald Niederreiter |
Publisher | : World Scientific |
Total Pages | : 460 |
Release | : 2002-12-03 |
Genre | : Mathematics |
ISBN | : 981448766X |
The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.
Author | : Wing C. Kwong |
Publisher | : CRC Press |
Total Pages | : 381 |
Release | : 2018-09-03 |
Genre | : Computers |
ISBN | : 1466567813 |
Although several books cover the coding theory of wireless communications and the hardware technologies and coding techniques of optical CDMA, no book has been specifically dedicated to optical coding theory—until now. Written by renowned authorities in the field, Optical Coding Theory with Prime gathers together in one volume the fundamentals and developments of optical coding theory, with a focus on families of prime codes, supplemented with several families of non-prime codes. The book also explores potential applications to coding-based optical systems and networks. Learn How to Construct and Analyze Optical Codes The authors use a theorem-proof approach, breaking down theories into digestible form so that readers can understand the main message without searching through tedious proofs. The book begins with the mathematical tools needed to understand and apply optical coding theory, from Galois fields and matrices to Gaussian and combinatorial analytical tools. Using a wealth of examples, the authors show how optical codes are constructed and analyzed, and detail their performance in a variety of applications. The book examines families of 1-D and 2-D asynchronous and synchronous, multilength, and 3-D prime codes, and some non-prime codes. Get a Working Knowledge of Optical Coding Theory to Help You Design Optical Systems and Networks Prerequisites include a basic knowledge of linear algebra and coding theory, as well as a foundation in probability and communications theory. This book draws on the authors’ extensive research to offer an authoritative reference on the emerging field of optical coding theory. In addition, it supplies a working knowledge of the theory and optical codes to help readers in the design of coding-based optical systems and networks. For more on the technological aspects of optical CDMA, see Optical Code Division Multiple Access: Fundamentals and Applications (CRC Press 2005).
Author | : Eiichi Bannai |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 303 |
Release | : 2021-02-22 |
Genre | : Mathematics |
ISBN | : 3110627736 |
This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.