Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.

This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

This book constitutes the refereed proceedings of the 2nd International Castle Meeting, ISMCTA 2008, Castillo de la Mota, Medina del Campo, Spain, September 2008. The 14 full papers and 5 invited papers presented were carefully reviewed and selected from 34 submissions for inclusion in the book. The papers cover network coding, quantum codes, group codes, codes and combinatorial structures, agebraic-geometry codes, as well as codes and applications.

This easy-to-read guide provides a concise introduction to the engineering background of modern communication systems, from mobile phones to data compression and storage. Background mathematics and specific engineering techniques are kept to a minimum so that only a basic knowledge of high-school mathematics is needed to understand the material covered. The authors begin with many practical applications in coding, including the repetition code, the Hamming code and the Huffman code. They then explain the corresponding information theory, from entropy and mutual information to channel capacity and the information transmission theorem. Finally, they provide insights into the connections between coding theory and other fields. Many worked examples are given throughout the book, using practical applications to illustrate theoretical definitions. Exercises are also included, enabling readers to double-check what they have learned and gain glimpses into more advanced topics, making this perfect for anyone who needs a quick introduction to the subject.

"Published in cooperation with NATO Emerging Security Challenges Division"--T.p.

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

The symposia in applied mathematics have been held under the auspices of the American Mathematical Society and others since 1967. This books connects coding theory with actual applications in consumer electronics and with other areas of mathematics. It covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science.

The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.

Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.