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Codes and Rings

Codes and Rings
Theory and Practice

by Minjia Shi,Adel Alahmadi,Patrick Solé

  • Publisher : Academic Press
  • Release : 2017-06-12
  • Pages : 318
  • ISBN : 0128133910
  • Language : En, Es, Fr & De
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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 Over Rings

Codes Over Rings
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2021
  • Pages : 329
  • ISBN : 9814468991
  • Language : En, Es, Fr & De
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Representation Theory, Group Rings, and Coding Theory

Representation Theory, Group Rings, and Coding Theory
Papers in Honor of S.D. Berman (1922-1987)

by M. Isaacs

  • Publisher : American Mathematical Soc.
  • Release : 1989
  • Pages : 357
  • ISBN : 0821850989
  • Language : En, Es, Fr & De
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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, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.

Rings, Modules and Codes

Rings, Modules and Codes
A Book

by André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier

  • Publisher : American Mathematical Soc.
  • Release : 2019-04-12
  • Pages : 355
  • ISBN : 1470441047
  • Language : En, Es, Fr & De
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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 with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.

Algebraic Coding Theory Over Finite Commutative Rings

Algebraic Coding Theory Over Finite Commutative Rings
A Book

by Steven T. Dougherty

  • Publisher : Springer
  • Release : 2017-07-04
  • Pages : 103
  • ISBN : 3319598066
  • Language : En, Es, Fr & De
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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, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.

Rings, Modules and Codes

Rings, Modules and Codes
Fifth International Conference, Noncommutative Rings and Their Applications, June 12-15, 2017, University Of Artois, Lens, France

by Andre Gerard Leroy

  • Publisher : Unknown Publisher
  • Release : 2019
  • Pages : 355
  • ISBN : 9781470452377
  • Language : En, Es, Fr & De
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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 with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed-Mull.

Concise Encyclopedia of Coding Theory

Concise Encyclopedia of Coding Theory
A Book

by W. Cary Huffman,Jon-Lark Kim,Patrick Solé

  • Publisher : CRC Press
  • Release : 2021-03-26
  • Pages : 998
  • ISBN : 1351375105
  • Language : En, Es, Fr & De
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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

Finite Commutative Rings and Their Applications

Finite Commutative Rings and Their Applications
A Book

by Gilberto Bini,Flaminio Flamini

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 176
  • ISBN : 1461509572
  • Language : En, Es, Fr & De
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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 book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

The Mathematical Theory of Coding

The Mathematical Theory of Coding
A Book

by Ian F. Blake,Ronald C. Mullin

  • Publisher : Academic Press
  • Release : 2014-05-10
  • Pages : 368
  • ISBN : 1483260593
  • Language : En, Es, Fr & De
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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 and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.

English Abstracts of Selected Articles from Soviet Bloc and Mainland China Technical Journals

English Abstracts of Selected Articles from Soviet Bloc and Mainland China Technical Journals
Bio-sciences

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1963
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Codes And Modular Forms: A Dictionary

Codes And Modular Forms: A Dictionary
A Book

by Minjia Shi,Youngju Choie,Anuradha Sharma,Patrick Sole

  • Publisher : World Scientific
  • Release : 2019-11-20
  • Pages : 232
  • ISBN : 9811212937
  • Language : En, Es, Fr & De
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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 sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level.

Advances in Ring Theory

Advances in Ring Theory
A Book

by Sergio R. López-Permouth,Dinh Van Huynh

  • Publisher : Springer Science & Business Media
  • Release : 2011-01-28
  • Pages : 345
  • ISBN : 9783034602860
  • Language : En, Es, Fr & De
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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 theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.

Approach

Approach
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1963
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The naval aviation safety review.

Finite Rings with Identity

Finite Rings with Identity
A Book

by Bernard R. McDonald,Bernard R.. McDonald,McDonald Bernard R

  • Publisher : Marcel Dekker Incorporated
  • Release : 1974
  • Pages : 429
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Quasi-Frobenius Rings

Quasi-Frobenius Rings
A Book

by W. K. Nicholson,M. F. Yousif

  • Publisher : Cambridge University Press
  • Release : 2003-09-08
  • Pages : 307
  • ISBN : 9780521815932
  • Language : En, Es, Fr & De
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Sample Text

Lectures on Modules and Rings

Lectures on Modules and Rings
A Book

by Tsit-Yuen Lam

  • Publisher : Springer Science & Business Media
  • Release : 1999
  • Pages : 557
  • ISBN : 9780387984285
  • Language : En, Es, Fr & De
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This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.

Cryptography and Coding

Cryptography and Coding
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1995
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Error-control Block Codes for Communications Engineers

Error-control Block Codes for Communications Engineers
A Book

by L. H. Charles Lee,Charles Lee

  • Publisher : Artech House Publishers
  • Release : 2000
  • Pages : 243
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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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 using error-control block codes.

Quaternary Codes

Quaternary Codes
A Book

by Zhexian Wan

  • Publisher : World Scientific
  • Release : 1997
  • Pages : 242
  • ISBN : 9789810232740
  • Language : En, Es, Fr & De
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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 study of quaternary codes, which constitute a rapidly growing area of coding theory. This book is based on the author's lectures in Xi'an, China and Lurid, Sweden and covets the most recent developments of this theory.

Codebreaker Code Book

Codebreaker Code Book
Prima Official Game Guide

by Prima Games

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 702
  • ISBN : 9780761555162
  • Language : En, Es, Fr & De
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· Over 50,000 codes for more than 1,300 titles available for your PS2. · A world of codes is at your fingertips: Infinite ammo, invincibility, level skipping, and more are just a click away! · CodeBreaker is a software program that opens exclusive codes for PS2 games. The print version of the CodeBreaker Code Book includes this software; you'll need to purchase a CodeBreaker disc in order to use the eGuide.