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5. Few Weights Codes
6. Linear Codes
7. Self-dual codes
8. Cyclic codes
9. Quasi-cyclic codes
10. Quasi-Twisted Codes
11. Generalized Quasi-Cyclic Codes
12. Skew Cyclic Codes
13. MDE Codes
14. Convoluted Codes
15. Character Sums
Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory.
New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area.
- Consolidates 20+ years of research in one volume, helping researchers save time in the evaluation of disparate literature
- Discusses duality formulas in the context of Frobenius rings
- Reviews decomposition of quasi-cyclic codes under ring action
- Evaluates the ideal and modular structure of skew-cyclic codes
- Supports applications in data compression, distributed storage, network coding, cryptography and across error-correction
Ring theorists principally at PhD and research level interested in applications and coding theorists interested in algebraic foundations. Computer scientists and cryptologists interested in the protection of information
- No. of pages:
- © Academic Press 2017
- 8th June 2017
- Academic Press
- Paperback ISBN:
- eBook ISBN:
"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
Minjia Shi is an Associate Professor of Mathematics in the School of Mathematical Sciences of Anhui University since 2012, P. R. China. He is the author of more than 60 journal papers and one book. He is interested in algebraic coding, cryptography and related fields.
School of Mathematical Sciences of Anhui University
Adel Alahmadi is Associate Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He is interested in algebraic geometry and ring theory.
King Abdulaziz University
Patrick Sole (Research Professor at Centre National de la Recherche Scientique). Sole received the Ingenieur and the Docteur Ingenieur degrees from Ecole Nationale Superieure des Telecommunications, Paris, France in 1984 and 1987, respectively, and the Habilitation Diriger des Recherches degree from Universite de Nice, Sophia Antipolis, France, in 1993. He has held visiting positions at Syracuse University, Syracuse, NY, during 1987-1989, Macquarie University, Sydney, Australia, during 1994-1996, and at Universite des Sciences et Techniques de Lille, Lille, France, during 1999-2000. He has been a permanent member of Centre National de la Recherche Scientique since 1989, and with the rank of research professor (Directeur de Recherche) since 1996. His research interests include coding theory (covering radius, codes over rings, geometric codes, quantum codes), interconnection networks (graph spectra, expanders), space time codes (lattices, theta series), and cryptography (Boolean functions). He is the author of more than a hundred and forty journal papers, and two books.
Centre National de la Recherche Scientique
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