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Codes and Rings
Theory and Practice
Reviews the theory of rings and presents applications pertaining to modern data compression, data encoding, and cryptography problems
Minjia Shi (Author), Adel Alahmadi (Author), Patrick Solé (Author)
9780128133880
Paperback, published 8 June 2017
318 pages
22.9 x 15.1 x 2.1 cm, 0.66 kg
"This book is a treatise for coding theorists interested in algebraic foundations, working cryptologists and researchers looking for applications of pure mathematics. The authors explain properties of special rings like local rings, Galois rings, chain rings, Frobenius rings and skew polynomial rings, which frequently occur in applications. They also discuss several bounds (such as the sphere-packing bound, a Plotkin-like bound, a Singleton-like bound) for codes over rings with respect to various metrics." --Mathematical Reviews Clippings "The authors point out how the subject is related to other fields e.g. combinatorics, number theory and ring theory. The book is very useful for references and can be also be used for the serious study of the subject. Ring theorists principally at PhD and research level, coding theorist interested in applications (computer scientists and cryptologists) could appreciate the collection and arrangement of research content of more than 250 references." --Zentralblatt MATH
Approx.302 pages
1. Introduction2. Motivation3. Rings4. Distances5. Few Weights Codes6. Linear Codes7. Self-dual codes8. Cyclic codes9. Quasi-cyclic codes10. Quasi-Twisted Codes11. Generalized Quasi-Cyclic Codes12. Skew Cyclic Codes13. MDE Codes14. Convoluted Codes15. Character Sums
Subject Areas: Applied mathematics [PBW]
