Codes and Rings

Theory and Practice Volume -
Erscheinungsjahr 2017
ISBN: 978-0-12-813388-0
Verlag: Elsevier Science

Buch, Englisch, 318 Seiten, Format (B × H): 228 mm x 151 mm, Gewicht: 660 g

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.

Zielgruppe

<p>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.</p>

Autoren/Hrsg.

Shi, Minjia

Alahmadi, Adel

Solé, Patrick

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

Solé, Patrick
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.

Alahmadi, Adel
Adel Alahmadi is Associate Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He is interested in algebraic geometry and ring theory.

Shi, Minjia
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.