An Introduction To Algebraic And Combinatorial Coding Theory
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An Introduction To Algebraic And Combinatorial Coding Theory
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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.
An Introduction To Algebraic And Combinatorial Coding Theory
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Author : Olga Moreira
language : en
Publisher:
Release Date : 2023-12
An Introduction To Algebraic And Combinatorial Coding Theory written by Olga Moreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12 with categories.
"An Introduction to Algebraic and Combinatorial Coding Theory" is a comprehensive book that offers a thorough exploration of the principles and techniques of coding theory. It serves as a valuable resource for readers interested in gaining a deeper understanding of error detection and correction in communication systems. With its well-structured chapters covering coding theory fundamentals, algebraic codes, cyclic codes, block codes, and advanced coding techniques, this book caters to the needs of students, researchers, and professionals in the field. It provides a solid foundation in coding theory and showcases its practical applications in various domains, including telecommunications, data storage, and cryptography.
A First Course In Coding Theory
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Author : Raymond Hill
language : en
Publisher: Oxford University Press
Release Date : 1986
A First Course In Coding Theory written by Raymond Hill and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Computers categories.
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.
An Introduction To Error Correcting Codes With Applications
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Author : Scott A. Vanstone
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
An Introduction To Error Correcting Codes With Applications written by Scott A. Vanstone 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 2013-04-18 with Technology & Engineering categories.
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.
Coding Theory
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Author : Jacobus H. van Lint
language : en
Publisher: Springer
Release Date : 2013-12-11
Coding Theory written by Jacobus 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 2013-12-11 with Mathematics categories.
Proceedings Of The Fourth International Congress On Mathematical Education
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Author : M. Zweng
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Proceedings Of The Fourth International Congress On Mathematical Education written by M. Zweng 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 2012-12-06 with Mathematics categories.
Henry O. Pollak Chairman of the International Program Committee Bell Laboratories Murray Hill, New Jersey, USA The Fourth International Congress on Mathematics Education was held in Berkeley, California, USA, August 10-16, 1980. Previous Congresses were held in Lyons in 1969, Exeter in 1972, and Karlsruhe in 1976. Attendance at Berkeley was about 1800 full and 500 associate members from about 90 countries; at least half of these come from outside of North America. About 450 persons participated in the program either as speakers or as presiders; approximately 40 percent of these came from the U.S. or Canada. There were four plenary addresses; they were delivered by Hans Freudenthal on major problems of mathematics education, Hermina Sinclair on the relationship between the learning of language and of mathematics, Seymour Papert on the computer as carrier of mathematical culture, and Hua Loo-Keng on popularising and applying mathematical methods. Gearge Polya was the honorary president of the Congress; illness prevented his planned attendence but he sent a brief presentation entitled, "Mathematics Improves the Mind". There was a full program of speakers, panelists, debates, miniconferences, and meetings of working and study groups. In addition, 18 major projects from around the world were invited to make presentations, and various groups representing special areas of concern had the opportunity to meet and to plan their future activities.
Algebraic Combinatorics
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Author : Chris Godsil
language : en
Publisher: CRC Press
Release Date : 1993-04-01
Algebraic Combinatorics written by Chris Godsil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-01 with Mathematics categories.
This book presents an introduction to some of the interactions between algebra and combinatorics. It focuses on the characteristic and matchings polynomials of a graph and introduces the theory of polynomial spaces. The book is intended for beginning graduate students in mathematics.
Software Engineer S Reference Book
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Author : John A McDermid
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Software Engineer S Reference Book written by John A McDermid and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.
Software Engineer's Reference Book provides the fundamental principles and general approaches, contemporary information, and applications for developing the software of computer systems. The book is comprised of three main parts, an epilogue, and a comprehensive index. The first part covers the theory of computer science and relevant mathematics. Topics under this section include logic, set theory, Turing machines, theory of computation, and computational complexity. Part II is a discussion of software development methods, techniques and technology primarily based around a conventional view of the software life cycle. Topics discussed include methods such as CORE, SSADM, and SREM, and formal methods including VDM and Z. Attention is also given to other technical activities in the life cycle including testing and prototyping. The final part describes the techniques and standards which are relevant in producing particular classes of application. The text will be of great use to software engineers, software project managers, and students of computer science.
Selected Topics In Information And Coding Theory
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Author : Isaac Woungang
language : en
Publisher: World Scientific
Release Date : 2010
Selected Topics In Information And Coding Theory written by Isaac Woungang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Pt. 1. Applications of coding theory to computational complexity. ch. 1. Linear complexity and related complexity measures / Arne Winterhof. ch. 2. Lattice and construction of high coding gain lattices from codes / Mohammd-Reza Sadeghi. ch. 3. Distributed space-time codes with low ML decoding complexity / G. Susinder Rajan and B. Sundar Rajan -- pt. 2. Methods of algebraic combinatorics in coding theory/codes construction and existence. ch. 4. Coding theory and algebraic combinatorics / Michael Huber. ch. 5. Block codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 6. LDPC and convolutional codes from matrix and group rings / Paul Hurley and Ted Hurley. ch. 7. Search for good linear codes in the class of quasi-cyclic and related codes / Nuh Aydin and Tsvetan Asamov -- pt. 3. Source coding/channel capacity/network coding. ch. 8. Applications of universal source coding to statistical analysis of time series / Boris Ryabko. ch. 9. Introduction to network coding for acyclic and cyclic networks / Ángela I. Barbero and Øyvind Ytrehus. ch. 10. Distributed joint source-channel coding on a multiple access channel / Vinod Sharma and R. Rajesh -- pt. 4. Other selected topics in information and coding theory. ch. 11. Low-density parity-check codes and the related performance analysis methods / Xudong Ma. ch. 12. Variable length codes and finite automata / Marie-Pierre Béal [und weitere]. ch. 13. Decoding and finding the minimum distance with Gröbner Bases : history and new insights / Stanislav Bulygin and Ruud Pellikaan. ch. 14. Cooperative diversity systems for wireless communication / Murat Uysal and Muhammad Mehboob Fareed. ch. 15. Public key cryptography and coding theory / Pascal Véron
Matroid Applications
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Author : Neil White
language : en
Publisher: Cambridge University Press
Release Date : 1992-03-05
Matroid Applications written by Neil White and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-05 with Mathematics categories.
This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).