A First Course in Coding Theory

Author: Raymond Hill

Publisher: Oxford University Press

ISBN: 9780198538035

Category: Technology & Engineering

Page: 251

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Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

A Course in Group Theory

Author: J. F. Humphreys

Publisher: Oxford University Press on Demand

ISBN: 9780198534594

Category: Business & Economics

Page: 279

View: 7323

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Each chapter ends with a summary of the material covered and notes on the history and development of group theory.

Information und Kommunikation

Grundlagen und Verfahren der Informationsübertragung

Author: Markus Hufschmid

Publisher: Springer Science & Business Media

ISBN: 3835101226

Category: Computers

Page: 294

View: 7408

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Das vorliegende Buch gibt einen Einblick in die grundlegenden Verfahren, die für eine effiziente und sichere Übertragung von Information notwendig sind. Es entstand im Rahmen von Vor lesungen, die ich in den vergangenen neun Jahren an der Fachhochschule beider Basel in Muttenz gehalten habe. Die einzelnen Themen Informationstheorie Kanalcodierung Stochastische Prozesse und Rauschen Digitale Modulationsverfahren B asisbandübertragung Analoge Modulationsverfahren Kryptologie sind so verfasst, dass sie weitgehend unabhängig voneinander und in beliebiger Reihenfolge durch gearbeitet werden können. Dies gilt insbesondere für den kryptologischen Teil, der keinerlei Vor kenntnisse der anderen Kapitel voraussetzt. Allerdings dürfte es von Vorteil sein, das Thema „Stochastische Prozesse und Rauschen" vor den Modulationsverfahren durchzuarbeiten. Ich bin der dezidierten Meinung, dass die Verfahren und Methoden der Informationsübertragung nur durch intensives Lösen von Problemen verstanden und verinnerlicht werden können. Dennoch enthält dieses Buch, aus Platzgründen, keine Aufgaben. Um dieses Dilemma zu lösen, steht dem Leser auf der begleitenden Webseite http://www.iiiformationsuebertragung.ch eine umfangreiche Aufgabensammlung zur Verfügung. An der gleichen Stelle können auch die dazugehörigen Musterlösungen heruntergeladen werden. Ich möchte die Studierenden jedoch davor warnen, der Versuchung zu erliegen, Aufgaben unter Zuhilfenahme der Lösungen zu bearbeiten. Das Nachvollziehen einer vorgegebenen Lösung erzielt nicht den gleichen Lemeffekt wie das selbstständige Lösen einer Aufgabe. Letzteres kann zwar zeitweise ein wenig frustrierend sein, dafür ist das nachfolgende Erfolgserlebnis um so grösser.

A First Course in Combinatorial Mathematics

Author: Ian Anderson

Publisher: Oxford University Press

ISBN: 9780198596738

Category: Science

Page: 134

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The spirit and aim of this book is to present a compact introduction to the basic combinatorial tools - such as recurrence relations, generating functions, incidence matrices, and the inclusion-exclusion principle - that will give the reader a flavour of the distinctive characteristics of this attractive and increasingly important branch of mathematics. A studly of block designs is followed by a brief mention of applications to coding theory. In this new edition, Steiner triple systems are constructed and S(5,8,24) is obtained via the Golay code of length 24. The final chapter combines together the three combinatorial structures of the Leech lattice, the Golay codes, and Steiner systems. Also in this edition, an application of the marriage theorem to score sequences of tournaments has been included.

Noncommutative Rings and Their Applications

Author: Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole

Publisher: American Mathematical Soc.

ISBN: 147041032X

Category: Mathematics

Page: 265

View: 8808

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This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras. Material from the course ``Foundations of Algebraic Coding Theory``, given by Steven Dougherty, is included and provides the reader with the history and background of coding theory as well as the interplay between coding theory and algebra. In module theory, many new results related to (almost) injective modules, injective hulls and automorphism-invariant modules are presented. Broad generalizations of classical projective covers are studied and category theory is used to describe the structure of some modules. In some papers related to more classical ring theory such as quasi duo rings or clean elements, new points of view on classical conjectures and standard open problems are given. Descriptions of codes over local commutative Frobenius rings are discussed, and a list of open problems in coding theory is presented within their context.

Error-correcting Codes and Finite Fields

Author: Oliver Pretzel

Publisher: Oxford University Press on Demand

ISBN: 9780192690678

Category: Computers

Page: 341

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This textbook is a reprint of Chapters 1-20 of the original hardback edition. It provides the reader with the tools necessary to implement modern error-processing schemes. The material on algebraic geometry and geometric Goppa codes, which is not part of a standard introductory course on coding theory, has been omitted. The book assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples whichmotivate and explain the theory. The book is in four parts. The first introduces the basic ideas of coding theory. The second and third cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. These parts are linked by their uses of Eulid's algorithm as a central technique. The fourth part treats classical Goppa codes.


Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

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An introduction to computational geometry for curves and surfaces

Author: Alan J. Davies,Philip Samuels

Publisher: Oxford University Press, USA


Category: Mathematics

Page: 205

View: 7989

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This is an ideal introductory textbook for undergraduates studying the applications of mathematics of curves and surfaces, especially in the generation of computer graphics and computer-aided design. Written by establised textbook authors, the text develops ideas in differential and computational geometry, with numerous exercises, solutions, and worked examples throughout providing the student with ample opportunity to test their knowledge. Only a basic knowledge of vector and matrix algebra is assumed, making it invaluable for those coming to this difficult subject for the first time.

Wave theory and applications

Author: David Russell Bland

Publisher: Oxford University Press, USA

ISBN: 9780198596547

Category: Education

Page: 317

View: 5719

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This textbook provides a modern introduction to wave theory and its applications to physical phenomena such as deep water waves, transmission lines, elasticity, and traffic flow. The author presents a broad coverage of the subject, including numerous exercises. Each of the main topics is described in detail with examples of their applications. These topics include the classical wave equation, dispersion, dissipation, interconnected waves, diffusive waves, and first and second order non-linear waves. The special attention paid to non-linear and elastic waves represents a major strength of the text, along with its inclusion of an entire chapter devoted to the use of characteristics and asymptotic expansions. Intended for advanced undergraduates, the book will also be of interest to instructors in mathematics, physics and engineering courses.

Database Systems Engineering

Author: R. P. Whittington

Publisher: Oxford University Press

ISBN: 9780198596660

Category: Data base management

Page: 430

View: 3980

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This textbook is an introduction to the principles and practice of database systems development and management. Its aim is to reflect the modern notion that information systems engineering has its own analysts, designers, and implementors comparable with any other engineering discipline. The book is based on courses at the University of York and will be suitable for all those coming to database systems for the first time. Starting from first principles, Dr Whittington discusses the analysis, design, and implementation of databases within the context of information systems. Topics covered include the relational model of databases, SQL (a relational database language), DBMS implementation, and the practicalities of selecting the logical, structural, and physical design of database systems. Throughout, key points are illustrated with practical examples, and numerous exercises will strengthen and further understanding. Consequently, this book will provide an invaluable andcomprehensive treatment of this increasingly important subject. By presenting the reader with a coherent treatment of database material within a sound engineering context, it better prepares the readers for the practical roles that the discipline demands.

Abstract Data Types

Their Specification, Representation, and Use

Author: Peter G. Thomas,Hugh Robinson,Judy Emms

Publisher: Oxford University Press

ISBN: 9780198596639

Category: Abstract data types (Computer science)

Page: 256

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This volume introduces abstract data types and their use in software engineering. Designed for self-study, the text offers over 100 exercises with fully worked solutions, and check point questions at critical places for monitoring progress. The authors, who base the text on their course at Open University (U.K.), lead students through designing, constructing, and implementing abstract data types using a number of simple but crucial concepts of software engineering such as stack, queue, and binary search trees. Two specification methods are studied: the axiomatic approach and the constructive approach. Illustrative examples throughout use Modula-2 and Ada, and three case studies are considered in detail.

Logic with Prolog

Author: Peter Gibbins

Publisher: Oxford University Press, USA


Category: Logic programming.

Page: 321

View: 4051

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This book is an introduction to the essential ideas of formal logic and to the new field of logic programming, which is beginning to have an impact on the traditional area of conventional software engineering. Logical concepts and how they may be implemented in the logic programming language Prolog are emphasized. The authors discuss parsers, pretty-printers, programming language interpreters, interactive proof-checkers, theorem-provers of various kinds, and implements versions of Prolog. The early part of the book deals with Prolog as a programming language, and how it can be used. The core of the book deals with the propositional and predicate calculi, which are treated conventionally, via natural deduction systems. The theory behind automatic theorem-proving is sketched. The last two chapters examine the logic of a specified small programming imperative language and the restricted logic of real Prolog. Philosophical questions are also considered.