Codes and Rings Theory and Practice Pure and Applied Mathematics Series
Auteurs : Shi Minjia, Alahmadi Adel, Solé Patrick
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.
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
Ring theorists principally at PhD and research level interested in applications and coding theorist interested in algebraic foundations. Computer scientists and cryptologists interested in the protection of information.
Adel Alahmadi is Associate Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He is interested in algebraic geometry and ring theory.
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.
- 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
Date de parution : 06-2017
Ouvrage de 318 p.
15x22.8 cm
Thèmes de Codes and Rings :
Mots-clés :
rings; cyclic codes; quasi-cyclic codes; quasi-twisted codes; skew cyclic codes; convoluted codes