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 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

Produk Detail:

  • Author : Minjia Shi
  • Publisher : Academic Press
  • Pages : 318 pages
  • ISBN : 0128133910
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKCodes and Rings

Codes and Rings

Codes and Rings
  • Author : Minjia Shi,Adel Alahmadi,Patrick Solé
  • Publisher : Academic Press
  • Release : 12 June 2017
GET THIS BOOKCodes 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 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,

Lectures on Modules and Rings

Lectures on Modules and Rings
  • Author : Tsit-Yuen Lam
  • Publisher : Springer Science & Business Media
  • Release : 28 February 1999
GET THIS BOOKLectures on Modules and Rings

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,

Rings, Modules and Codes

Rings, Modules and Codes
  • Author : André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier
  • Publisher : American Mathematical Soc.
  • Release : 12 April 2019
GET THIS BOOKRings, 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 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

The Mathematical Theory of Coding

The Mathematical Theory of Coding
  • Author : Ian F. Blake,Ronald C. Mullin
  • Publisher : Academic Press
  • Release : 10 May 2014
GET THIS BOOKThe 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 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

Exercises in Modules and Rings

Exercises in Modules and Rings
  • Author : T.Y. Lam
  • Publisher : Springer Science & Business Media
  • Release : 08 December 2009
GET THIS BOOKExercises in Modules and Rings

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.

Quaternary Codes

Quaternary Codes
  • Author : Zhexian Wan
  • Publisher : World Scientific
  • Release : 28 February 1997
GET THIS BOOKQuaternary 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 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

Codes And Modular Forms: A Dictionary

Codes And Modular Forms: A Dictionary
  • Author : Minjia Shi,Youngju Choie,Anuradha Sharma,Patrick Sole
  • Publisher : World Scientific
  • Release : 20 November 2019
GET THIS BOOKCodes 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 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

Modules and Rings

Modules and Rings
  • Author : John Dauns
  • Publisher : Cambridge University Press
  • Release : 28 October 1994
GET THIS BOOKModules and Rings

This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products.

Algebraic Coding Theory Over Finite Commutative Rings

Algebraic Coding Theory Over Finite Commutative Rings
  • Author : Steven T. Dougherty
  • Publisher : Springer
  • Release : 04 July 2017
GET THIS BOOKAlgebraic 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, 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