W. Cary Huffman, Vera Pless

Fundamentals of Error Correcting Codes

Description

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, much coverage is included of recent techniques which until now 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.

Chapter Contents

Preface; 1. Basic concepts of linear codes; 2. Bounds on size of codes; 3. Finite fields; 4. Cyclic codes; 5. BCH and Reed-Soloman codes; 6. Duadic codes; 7. Weight distributions; 8. Designs; 9. Self-dual codes; 10. Some favourite self-dual codes; 11. Covering radius and cosets; 12. Codes over Z4; 13. Codes from algebraic geometry; 14. Convolutional codes; 15. Soft decision and iterative decoding; Bibliography; Index.

ISBN: 0-521-78280-5
Binding: Hardback
Pages: 850
Figures: 10 line diagrams 20 tables

Not yet published - available from January 2003

Edward Slowik

Cartesian Spacetime
Descartes' Physics and the Relational Theory of Space and Motion

January 2002, ISBN 1-4020-0265-3, Hardbound

Although Descartes' natural philosophy marked an advance in the development of modern science, many critics over the years, such as Newton, have rejected his particular `relational' theory of space and motion. Nevertheless, it is also true that most historians and philosophers have not sufficiently investigated the viability of the Cartesian theory.

This book explores, consequently, the success of the arguments against Descartes' theory of space and motion by determining if it is possible to formulate a version that can eliminate its alleged problems. In essence, this book comprises the first sustained attempt to construct a consistent `Cartesian' spacetime theory: that is, a theory of space and time that consistently incorporates Descartes' various physical and metaphysical concepts.

Intended for students in the history of philosophy and science, this study reveals the sophisticated insights, and often quite successful elements, in Descartes' unjustly neglected relational theory of space and motion.

Contents

Preface. Introduction. Part I: Descartes, Newton, and the Absolute/Relational Spacetime Debate. 1. Newton's De Gravitatione Argument Against Cartesian Dynamics. 2. The Structure of Spacetime Theories. Part II: Cartesian Physics. 3. The Cartesian Natural Laws. 4. Matter and Substance in the Cartesian Universe. 5. Quantity of Motion: The Function and Origin of the Cartesian Conservation Principle. Part III: Constructing a Cartesian Spacetime. 6. Relational Spacetime and Cartesian Dynamics. 7. The Kinematic Logic of Relational Transfer: An Unwritten Chapter in the History of Cartesian Motion. 8. Constructing a Cartesian Dynamics Without `Fixed' Reference Frames: Collisions in the Center-of-Mass Frame. 9. Constructing a Cartesian Dynamics With `Fixed' Reference Frames: The `Kinematics of Mechanisms' Theory. Conclusion. Bibliography. Index.

R. Beattie, H.-P. Butzmann

Convergence Structures and Applications
to Functional Analysis

March 2002, ISBN 1-4020-0566-0, Hardbound

This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus.

The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces.

Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result.

Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.

Contents

Introduction. 1. Convergence spaces. 2. Uniform convergence spaces. 3. Convergence vector spaces. 4. Duality. 5. Hahn-Banach extension theorems. 6. The closed graph theorem. 7. The Banach-Steinhaus theorem. 8. Duality theory for convergence groups. Bibliography. List of Notations. Index

Mario Blaum, Patrick G. Farrell, Henk C.A. van Tilborg

Information, Coding and Mathematics

May 2002, ISBN 1-4020-7079-9, Hardbound

Information, Coding and Mathematics is a classic reference for both professional and academic researchers working in error-correction coding and decoding, Shannon theory, cryptography, digital communications, information security, and electronic engineering.

The work represents a collection of contributions from leading experts in turbo coding, cryptography and sequences, Shannon theory and coding bounds, and decoding theory and applications. All of the contributors have individually and collectively dedicated their work as a tribute to the outstanding work of Robert J. McEliece.

Information, Coding and Mathematics covers the latest advances in the widely used and rapidly developing field of information and communication technology.

Contents and Contributors

Preface. 1. A Computational Theory of Surprise; P. Baldi. 2. Dynamic Key Distribution Using MDS Codes; L. Xu. 3. Worst-Case Mutual Information Trajectories in Concatenated Codes with Asymptotic Interleavers; D. Divsalar, S. Shamai. 4. Results to get Maximal Quasihermitian Curves. New possibilities for AG Codes; R.J. McEliece, M.C. Rodriguez-Palanquex. 5. On Asymmetric Error Detection with Feedback; P. Oprisan, B. Bose. 6. Cryptanalysis of Block Ciphers and Weight Divisibility of Some Binary Codes; A. Canteaut, et al. 7. Sloppy Alice attacks! Adaptive chosen ciphertext attacks on the McEliece Public-Key Cryptosystem; E.R. Verheul, et al. 8. Reducible Rank Codes and Applications to Cryptography; E.M. Gabidulin, et al. 9. On a Boolean Maximization Problem; S.W. Golomb, W. Chu. 10. On the Security of the McEliece Public-Key Cryptosystem; N. Sendrier. 11. Performance of MIMO Space Time-Coding with Discrete Modulations on Flat Fading Channels; J.-F. Chen. 12. Coding for Slow-Frequency-Hop Transmission: Variations on a Theme of McEliece; T.G. Macdonald, M.B. Pursley. 13. On Graph Constructions for LDPC Codes by Quasi-Cyclic Extension; R.M. Tanner. 14. On the Channel Memory-Diversity Tradeoff in Communication Systems; A.P. Worthen, W.E. Stark. 15. Duality, Dirty Paper Coding, and Capacity for Multiuser Wireless Channels; N. Jindal, et al. 16. Stability Analysis of the Turbo Decoding Algorithm Using Max-Log-MAP; W.-S. Wu, et al. 17. Recursive List Decoding for Reed-Muller Codes and their Subcodes; I. Dumer, K. Shabunov. 18. Adaptive Soft-Decision Decoding In Two Dimensions; X.-H. Peng, et al. 19. On the Theory of Linear Trellises; R. Koetter, A. Vardy. 20. Coding Over Graphs; A. Jiang, J. Bruck. 21. On Approaching the Capacity of Finite-State Intersymbol Interference Channels; J.B. Soriaga, et al.

Alexander V. Mikhalev, Gunter F. Pilz

The Concise Handbook of Algebra

May 2002, ISBN 0-7923-7072-4, Hardbound

The Concise Handbook of Algebra provides a succinct, but thorough treatment of algebra. The editors have gone to great lengths to capture the core essence of the different ideas, concepts and results that make up algebra as we know it today. In a collection that spans about 150 sections organized in 9 chapters, algebraists are provided with a standard knowledge set for their areas of expertise.

Other readers meanwhile, are equipped with a quick and dependable reference to the area as a whole. All of this is presented uniformally with cross-references linking the sections.

The target audience consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of the selected topics.

Contents and Contributors