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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.

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"Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research Editor bio W. Cary Huffman (1948-) received his PhD in mathematics from the California Institute of Technology in 1974. He taught at Dartmouth College (1974 - 1976) as a John Wesley Young Research Instructor and then at Union College (1976 - 1978). In 1978, he joined the Department of Mathematics and Statistics at Loyola University Chicago, continuing there until his retirement in 2018; he is now professor emeritus. He served as that department's chair from 1986 to 1992. He is co-editor of the Handbook of Coding Theory and co-author of Fundamentals of Error-Correcting Codes, both with Vera Pless. In addition, he has published numerous papers in finite group theory, combinatorics, and algebraic coding theory. Jon-Lark Kim received his Ph.D. in 2002 from Department of Math of the University of Illinois at Chicago. He was an Associate Professor at the University of Louisville until 2012. He is currently professor at Math Department of Sogang University in Seoul. He has authored more than fifty research papers and one book on Coding Theory. He is the recipient of the 2004 Kirkman medal from the Institute of Combinatorics and its Applications. His research interests include Coding Theory, Cryptography, Combinatorics, Bioinformatics, and Artificial Intelligence. Patrick Solé (1960-) received the Ingénieur and the Docteur Ingénieur degrees from Ecole Nationale Supérieure des Télécommunications, Paris, France in 1984 and 1987, respectively, and the Habilitation à Diriger des Recherches degree from University of Nice Sophia-Antipolis, France, in 1993"--

Coding theory

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This is the proceedings volume of the International Centre for Pure and Applied Mathematics Summer School course held in Ankara, Turkey, in August 2008. Contributors include Bozta?, Udaya, Dinh, Ling, L�opez-Permouth, Szabo, Honold, Landjev and Wood. The aim is to present a survey in fundamental areas and highlight some recent results.

Coding theory --- Rings (Algebra) --- Quasi-Frobenius rings --- Number theory