Codes and Rings : Theory and Practice - Shi

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Codes and Rings

Theory and Practice

By: Shi, Sole, Alahmadi

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Paperback | 8 June 2017 | Edition Number 1

At a Glance

Paperback
318 Pages

Dimensions(cm)
22.86 x 14.61 x 1.91

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RRP $233.95

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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.

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

Industry Reviews

"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

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