Codes and Rings

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. 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.

• 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

"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