› › An Algebraic Approach To The Association Schemes Of Coding Theory

An Algebraic Approach to Association Schemes

Author : Paul-Hermann Zieschang

Publisher : Springer

Page : 201 pages

File Size : 20,29 MB

Release : 2006-11-13

Category : Mathematics

ISBN : 3540685235

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Book Description

The primary object of the lecture notes is to develop a treatment of association schemes analogous to that which has been so successful in the theory of finite groups. The main chapters are decomposition theory, representation theory, and the theory of generators. Tits buildings come into play when the theory of generators is developed. Here, the buildings play the role which, in group theory, is played by the Coxeter groups. - The text is intended for students as well as for researchers in algebra, in particular in algebraic combinatorics.



Algebraic Combinatorics

Author : Eiichi Bannai

Publisher : Walter de Gruyter GmbH & Co KG

Page : 303 pages

File Size : 31,29 MB

Release : 2021-02-22

Category : Mathematics

ISBN : 3110627736

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Book Description

This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.



An Introduction to Algebraic and Combinatorial Coding Theory

Author : Ian F. Blake

Publisher : Academic Press

Page : 244 pages

File Size : 20,28 MB

Release : 2014-05-10

Category : Mathematics

ISBN : 1483260291

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Book Description

An Introduction to Algebraic and Combinatorial Coding Theory focuses on the principles, operations, and approaches involved in the combinatorial coding theory, including linear transformations, chain groups, vector spaces, and combinatorial constructions. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on quadratic residues and codes, self-dual and quasicyclic codes, balanced incomplete block designs and codes, polynomial approach to coding, and linear transformations of vector spaces over finite fields. The text then examines coding and combinatorics, including chains and chain groups, equidistant codes, matroids, graphs, and coding, matroids, and dual chain groups. The manuscript also ponders on Möbius inversion formula, Lucas's theorem, and Mathieu groups. The publication is a valuable source of information for mathematicians and researchers interested in the combinatorial coding theory.





Introduction To Algebraic Coding Theory

Author : Tzuong-tsieng Moh

Publisher : World Scientific

Page : 266 pages

File Size : 37,19 MB

Release : 2022-02-18

Category : Mathematics

ISBN : 9811220980

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Book Description

In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.



Poset Codes: Partial Orders, Metrics and Coding Theory

Author : Marcelo Firer

Publisher : Springer

Page : 133 pages

File Size : 12,49 MB

Release : 2018-11-01

Category : Mathematics

ISBN : 3319938215

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Book Description

This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, were first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards coding theory for poset metrics and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven results. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.



Applications of Hypergroups and Related Measure Algebras

Author :

Publisher : American Mathematical Soc.

Page : 458 pages

File Size : 20,91 MB

Release : 1995-02-28

Category : Mathematics

ISBN : 0821802976

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Book Description

`The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.



Coding Theory and Applications

Author : Angela Barbero

Publisher : Springer Science & Business Media

Page : 204 pages

File Size : 39,31 MB

Release : 2008-09-05

Category : Computers

ISBN : 354087447X

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Book Description

This book constitutes the refereed proceedings of the 2nd International Castle Meeting, ISMCTA 2008, Castillo de la Mota, Medina del Campo, Spain, September 2008. The 14 full papers and 5 invited papers presented were carefully reviewed and selected from 34 submissions for inclusion in the book. The papers cover network coding, quantum codes, group codes, codes and combinatorial structures, agebraic-geometry codes, as well as codes and applications.



Erdos-Ko-Rado Theorems: Algebraic Approaches

Author : Christopher Godsil

Publisher : Cambridge University Press

Page : 353 pages

File Size : 36,63 MB

Release : 2016

Category : Mathematics

ISBN : 1107128447

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Book Description

Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.



Introduction to Global Variational Geometry

Author : Demeter Krupka

Publisher : Elsevier

Page : 787 pages

File Size : 36,65 MB

Release : 2000-04-01

Category : Mathematics

ISBN : 0080954235

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Book Description

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics- Analysis on manifolds- Differential forms on jet spaces - Global variational functionals- Euler-Lagrange mapping - Helmholtz form and the inverse problem- Symmetries and the Noether's theory of conservation laws- Regularity and the Hamilton theory- Variational sequences - Differential invariants and natural variational principles- First book on the geometric foundations of Lagrange structures- New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity- Basic structures and tools: global analysis, smooth manifolds, fibred spaces