图书简介
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 boundsPart II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphsPart 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.FeaturesSuitable for students and researchers in a wide range of mathematical disciplinesContains many examples and referencesMost topics take the reader to the frontiers of research
Part I. Coding Fundamentals
1. Basics of Coding TheoryW. Cary Huffman, Jon-Lark Kim, and Patrick Solé
2. Cyclic Codes over Finite FieldsCunsheng Ding
3. Construction and Classification of Codes.Patric R. J. Östergård
4. Self-Dual CodesStefka Bouyuklieva
5. Codes and DesignsVladimir D. Tonchev
6. Codes over RingsSteven T. Dougherty
7. Quasi-Cyclic CodesCem Güneri, San Ling, and Buket Özkaya
8. Introduction to Skew-Polynomial Rings and Skew-Cyclic CodesHeide Gluesing-Luerssen
9. Additive Cyclic CodesJürgen Bierbrauer, Stefano Marcugini, and Fernanda Pambianco
10. Convolutional CodesJulia Lieb, Raquel Pinto, and Joachim Rosenthal
11. Rank-Metric CodesElisa Gorla
12. Linear Programming BoundsPeter Boyvalenkov and Danyo Danev
13. Semidefinite Programming Bounds for Error-Correcting CodesFrank Vallentin
Part II. Families of Codes
14. Coding Theory and Galois GeometriesLeo Storme
15. Algebraic Geometry Codes and Some ApplicationsAlain Couvreur and Hugues Randriambololona
16. Codes in Group AlgebrasWolfgang Willems
17. Constacyclic Codes over Finite Commutative Chain RingsHai Q. Dinh and Sergio R. López-Permouth
18. Weight Distribution of Trace Codes over Finite Rings
Minjia Shi
19. Two-Weight CodesAndries E. Brouwer
20. Linear Codes from FunctionsSihem Mesnager
21. Codes over Graphs Christine A. Kelley
Part III. Applications
22. Alternative MetricsMarcelo Firer
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