Concise encyclopedia of coding theory
著者
書誌事項
Concise encyclopedia of coding theory
CRC Press, 2021
- : hbk
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注記
Includes bibliographical references ( p. 823-939) and index
内容説明・目次
内容説明
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry.
Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.
The book is divided into three parts:
Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds
Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs
Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography.
Features
Suitable for students and researchers in a wide range of mathematical disciplines
Contains many examples and references
Most topics take the reader to the frontiers of research
目次
Part I. Coding Fundamentals. 1. Basics of Coding Theory. 2. Cyclic Codes over Finite Fields. 3. Construction and Classification of Codes. 4. Self-Dual Codes. 5. Codes and Designs. 6. Codes over Rings. 7. Quasi-Cyclic Codes. 8. Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes. 9. Additive Cyclic Codes. 10. Convolutional Codes. 11. Rank-Metric Codes. 12. Linear Programming Bounds. 13. Semidefinite Programming Bounds for Error-Correcting Codes. Part II. Families of Codes. 14. Coding Theory and Galois Geometries. 15. Algebraic Geometry Codes and Some Applications. 16. Codes in Group Algebras. 17. Constacyclic Codes over Finite Commutative Chain Rings. 18. Weight Distribution of Trace Codes over Finite Rings. 19. Two-Weight Codes. 20. Linear Codes from Functions. 21. Codes over Graphs. Part III. Applications. 22. Alternative Metrics. 23. Algorithmic Methods. 24. Interpolation Decoding. 25. Pseudo-Noise Sequences. 26. Lattice Coding. 27. Quantum Error-Control Codes. 28. Space-Time Coding. 29. Network Codes. 30. Coding for Erasures and Fountain Codes. 31. Codes for Distributed Storage. 32. Polar Codes. 33. Secret Sharing with Linear Codes. 34. Code-Based Cryptography. Bibliography. Index.
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