codes and rings

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Codes and Rings
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Publisher : Academic Press
Release Date :
ISBN 10 : 0128133910
Pages : 318 pages
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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

Codes and Rings

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

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Codes Over Rings

Download or read online Codes Over Rings written by Anonim, published by Unknown which was released on . Get Codes Over Rings Books now! Available in PDF, ePub and Kindle.

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Representation Theory  Group Rings  and Coding Theory

This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory,

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Rings  Modules and Codes

This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory

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Algebraic Coding Theory Over Finite Commutative Rings

This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception,

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Rings  Modules and Codes

This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12-15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module

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Concise Encyclopedia of Coding Theory

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

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Finite Commutative Rings and Their Applications

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The

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The Mathematical Theory of Coding

The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues

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Quaternary Codes

In recent years quaternary codes have attracted the attention of the coding community as several notorious binary nonlinear codes containing more codewords than any known linear codes were found to be binary images under the Gray map of linear codes over Z 4 This discovery opens the way for a broader

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Codes And Modular Forms  A Dictionary

There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide

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Higher Power Residue Codes Over Galois Rings and Related Lattices

Download or read online Higher Power Residue Codes Over Galois Rings and Related Lattices written by Mehrdad Ahmadzadeh Raji, published by Unknown which was released on 2002. Get Higher Power Residue Codes Over Galois Rings and Related Lattices Books now! Available in PDF, ePub and Kindle.

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Advances in Ring Theory

This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring

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Cryptography and Coding

Download or read online Cryptography and Coding written by Anonim, published by Unknown which was released on 1995. Get Cryptography and Coding Books now! Available in PDF, ePub and Kindle.

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Error control Block Codes for Communications Engineers

Put the latest practical information available on error-control block coding and decoding to work for you with this handy new reference. It examines in detail linear block codes, cyclic codes, BCH codes, RS codes, and mutlilevel block-coded modulation and provides valuable simulation results to save you time in understanding and

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