Selected Unsolved Problems In Coding Theory

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Selected Unsolved Problems in Coding Theory

Author : David Joyner
Publisher : Springer Science & Business Media
ISBN 13 : 0817682562
Total Pages : 211 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Selected Unsolved Problems in Coding Theory by : David Joyner

Download or read book Selected Unsolved Problems in Coding Theory written by David Joyner and published by Springer Science & Business Media. This book was released on 2011-08-26 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.

Selected Topics In Information And Coding Theory

Author : Isaac Woungang
Publisher : World Scientific
ISBN 13 : 981446919X
Total Pages : 725 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Selected Topics In Information And Coding Theory by : Isaac Woungang

Download or read book Selected Topics In Information And Coding Theory written by Isaac Woungang and published by World Scientific. This book was released on 2010-02-26 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.

Coding Theory And Cryptology

Author : Harald Niederreiter
Publisher : World Scientific
ISBN 13 : 981448766X
Total Pages : 460 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Coding Theory And Cryptology by : Harald Niederreiter

Download or read book Coding Theory And Cryptology written by Harald Niederreiter and published by World Scientific. This book was released on 2002-12-03 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.

The Theory of Information and Coding

Author : R. J. McEliece
Publisher : Cambridge University Press
ISBN 13 : 9780521831857
Total Pages : 414 pages
Book Rating : 4.8/5 (318 download)

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Book Synopsis The Theory of Information and Coding by : R. J. McEliece

Download or read book The Theory of Information and Coding written by R. J. McEliece and published by Cambridge University Press. This book was released on 2004-07-15 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Student edition of the classic text in information and coding theory

Introduction to Coding Theory

Author : Ron Roth
Publisher : Cambridge University Press
ISBN 13 : 9780521845045
Total Pages : 592 pages
Book Rating : 4.8/5 (45 download)

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Book Synopsis Introduction to Coding Theory by : Ron Roth

Download or read book Introduction to Coding Theory written by Ron Roth and published by Cambridge University Press. This book was released on 2006-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

Algebraic Geometry Modeling in Information Theory

Author : Edgar Martinez-Moro
Publisher : World Scientific
ISBN 13 : 9814335762
Total Pages : 334 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Algebraic Geometry Modeling in Information Theory by : Edgar Martinez-Moro

Download or read book Algebraic Geometry Modeling in Information Theory written by Edgar Martinez-Moro and published by World Scientific. This book was released on 2013 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.

The Mathematical Theory of Coding

Author : Ian F. Blake
Publisher : Academic Press
ISBN 13 : 1483260593
Total Pages : 369 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Mathematical Theory of Coding by : Ian F. Blake

Download or read book The Mathematical Theory of Coding written by Ian F. Blake and published by Academic Press. This book was released on 2014-05-10 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Error Correcting Codes

Author : Florence Jessie MacWilliams
Publisher :
ISBN 13 :
Total Pages : 762 pages
Book Rating : 4.:/5 (163 download)

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Book Synopsis The Theory of Error Correcting Codes by : Florence Jessie MacWilliams

Download or read book The Theory of Error Correcting Codes written by Florence Jessie MacWilliams and published by . This book was released on 1978 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adventures in Graph Theory

Author : W. David Joyner
Publisher : Birkhäuser
ISBN 13 : 3319683837
Total Pages : 344 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Adventures in Graph Theory by : W. David Joyner

Download or read book Adventures in Graph Theory written by W. David Joyner and published by Birkhäuser. This book was released on 2017-12-28 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

Mathematicians Playing Games

Author : Jon-Lark Kim
Publisher : CRC Press
ISBN 13 : 1003807844
Total Pages : 135 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Mathematicians Playing Games by : Jon-Lark Kim

Download or read book Mathematicians Playing Games written by Jon-Lark Kim and published by CRC Press. This book was released on 2023-12-14 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features Suitable for anyone with an interest in games and mathematics. Could be especially useful to middle and high school students and their teachers Partial solutions to the various exercises included in the book.

Noncommutative Rings and Their Applications

Author : Steven Dougherty
Publisher : American Mathematical Soc.
ISBN 13 : 147041032X
Total Pages : 280 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Noncommutative Rings and Their Applications by : Steven Dougherty

Download or read book Noncommutative Rings and Their Applications written by Steven Dougherty and published by American Mathematical Soc.. This book was released on 2015-02-20 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exercises in Applied Mathematics

Author : Daniel Alpay
Publisher : Springer Nature
ISBN 13 : 3031518225
Total Pages : 694 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Exercises in Applied Mathematics by : Daniel Alpay

Download or read book Exercises in Applied Mathematics written by Daniel Alpay and published by Springer Nature. This book was released on with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sampling Theory, a Renaissance

Author : Götz E. Pfander
Publisher : Birkhäuser
ISBN 13 : 3319197495
Total Pages : 532 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Sampling Theory, a Renaissance by : Götz E. Pfander

Download or read book Sampling Theory, a Renaissance written by Götz E. Pfander and published by Birkhäuser. This book was released on 2015-12-08 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central pillar of Sampling Theory. The growing need to efficiently obtain precise and tailored digital representations of complex objects and phenomena requires the maturation of available tools in Sampling Theory as well as the development of complementary, novel mathematical theories. Today, research themes such as Compressed Sensing and Frame Theory re-energize the broad area of Sampling Theory. This volume illustrates the renaissance that the area of Sampling Theory is currently experiencing. It touches upon trendsetting areas such as Compressed Sensing, Finite Frames, Parametric Partial Differential Equations, Quantization, Finite Rate of Innovation, System Theory, as well as sampling in Geometry and Algebraic Topology.

Sampling: Theory and Applications

Author : Stephen D. Casey
Publisher : Springer Nature
ISBN 13 : 3030362914
Total Pages : 210 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Sampling: Theory and Applications by : Stephen D. Casey

Download or read book Sampling: Theory and Applications written by Stephen D. Casey and published by Springer Nature. This book was released on 2020-05-20 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters of this volume are based on talks given at the eleventh international Sampling Theory and Applications conference held in 2015 at American University in Washington, D.C. The papers highlight state-of-the-art advances and trends in sampling theory and related areas of application, such as signal and image processing. Chapters have been written by prominent mathematicians, applied scientists, and engineers with an expertise in sampling theory. Claude Shannon’s 100th birthday is also celebrated, including an introductory essay that highlights Shannon’s profound influence on the field. The topics covered include both theory and applications, such as: • Compressed sensing• Non-uniform and wave sampling• A-to-D conversion• Finite rate of innovation• Time-frequency analysis• Operator theory• Mobile sampling issues Sampling: Theory and Applications is ideal for mathematicians, engineers, and applied scientists working in sampling theory or related areas.

New Perspectives on Approximation and Sampling Theory

Author : Ahmed I. Zayed
Publisher : Springer
ISBN 13 : 3319088017
Total Pages : 487 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis New Perspectives on Approximation and Sampling Theory by : Ahmed I. Zayed

Download or read book New Perspectives on Approximation and Sampling Theory written by Ahmed I. Zayed and published by Springer. This book was released on 2014-11-03 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer’s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing.

Metrics, Norms, Inner Products, and Operator Theory

Author : Christopher Heil
Publisher : Birkhäuser
ISBN 13 : 3319653229
Total Pages : 374 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Metrics, Norms, Inner Products, and Operator Theory by : Christopher Heil

Download or read book Metrics, Norms, Inner Products, and Operator Theory written by Christopher Heil and published by Birkhäuser. This book was released on 2018-08-28 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students. Key features: Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter. Suitable for undergraduate-level courses; no familiarity with measure theory is required. Extensive exercises complement the text and provide opportunities for learning by doing. A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.

Stochastic Models, Information Theory, and Lie Groups, Volume 2

Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
ISBN 13 : 0817649433
Total Pages : 460 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stochastic Models, Information Theory, and Lie Groups, Volume 2 by : Gregory S. Chirikjian

Download or read book Stochastic Models, Information Theory, and Lie Groups, Volume 2 written by Gregory S. Chirikjian and published by Springer Science & Business Media. This book was released on 2011-11-15 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.