Poset Codes Partial Orders Metrics And Coding Theory

Author : Marcelo Firer,Marcelo Muniz S. Alves,Jerry Anderson Pinheiro,Luciano Panek
Publisher : Springer
Page : 127 pages
File Size : 48,7 Mb
Release : 2018-11-01
Category : Mathematics
ISBN : 9783319938219

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Poset Codes: Partial Orders, Metrics and Coding Theory by Marcelo Firer,Marcelo Muniz S. Alves,Jerry Anderson Pinheiro,Luciano Panek Pdf

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.

Author : Aiden A. Bruen,David L. Wehlau
Publisher : American Mathematical Soc.
Page : 255 pages
File Size : 41,7 Mb
Release : 2010-09-03
Category : Mathematics
ISBN : 9780821849569

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Error-Correcting Codes, Finite Geometries and Cryptography by Aiden A. Bruen,David L. Wehlau Pdf

This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, On, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007. The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0, 1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes. Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.

Author : Sudhakar Radhakrishnan,Sudev Naduvath
Publisher : BoD – Books on Demand
Page : 142 pages
File Size : 49,9 Mb
Release : 2022-05-25
Category : Computers
ISBN : 9781839694097

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Coding Theory by Sudhakar Radhakrishnan,Sudev Naduvath Pdf

This book explores the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavors. It consists of seven chapters that address such topics as applications of coding theory in networking and cryptography, wireless sensor nodes in wireless body area networks, the construction of linear codes, and more.

Author : Jacobus H. van Lint
Publisher : Springer
Page : 145 pages
File Size : 50,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662207123

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Coding Theory by Jacobus H. van Lint Pdf

Author : Jurgen Bierbrauer
Publisher : CRC Press
Page : 390 pages
File Size : 53,5 Mb
Release : 2004-08-17
Category : Mathematics
ISBN : 9781482296372

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Introduction to Coding Theory by Jurgen Bierbrauer Pdf

Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration. Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed. Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.

Author : Marco Fattore,Rainer Bruggemann
Publisher : Springer
Page : 0 pages
File Size : 51,5 Mb
Release : 2016-12-27
Category : Science
ISBN : 3319454196

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Partial Order Concepts in Applied Sciences by Marco Fattore,Rainer Bruggemann Pdf

TThis book illustrates recent advances in applications of partial order theory and Hasse diagram techniques to data analysis, mainly in the socio-economic and environmental sciences. For years, partial order theory has been considered a fundamental branch of mathematics of only theoretical interest. In recent years, its effectiveness as a tool for data analysis is increasingly being realized and many applications of partially ordered sets to real problems in statistics and applied sciences have appeared. Main examples pertain to the analysis of complex and multidimensional systems of ordinal data and to problems of multi-criteria decision making, so relevant in social and environmental sciences. Partial Order Concepts in Applied Sciences presents new theoretical and methodological developments in partial order for data analysis, together with a wide range of applications to different topics: multidimensional poverty, economic development, inequality measurement, ecology and pollution, and biology, to mention a few. The book is of interest for applied mathematicians, statisticians, social scientists, environmental scientists and all those aiming at keeping pace with innovation in this interesting, growing and promising research field.

Author : Jacobus H. van Lint
Publisher : Unknown
Page : 294 pages
File Size : 55,5 Mb
Release : 1972
Category : Coding theory
ISBN : LCCN:73083239

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Coding Theory by Jacobus H. van Lint Pdf

Author : Avi Wigderson
Publisher : Princeton University Press
Page : 434 pages
File Size : 49,8 Mb
Release : 2019-10-29
Category : Computers
ISBN : 9780691189130

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Mathematics and Computation by Avi Wigderson Pdf

An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Author : Dirk Hofmann,Gavin J. Seal,Walter Tholen
Publisher : Cambridge University Press
Page : 523 pages
File Size : 45,7 Mb
Release : 2014-07-31
Category : Mathematics
ISBN : 9781107063945

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Monoidal Topology by Dirk Hofmann,Gavin J. Seal,Walter Tholen Pdf

Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 42,6 Mb
Release : 1977-05-23
Category : Mathematics
ISBN : 9780080570426

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Elements of Set Theory by Herbert B. Enderton Pdf

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Author : W. Cary Huffman,Jon-Lark Kim,Patrick Solé
Publisher : CRC Press
Page : 998 pages
File Size : 48,6 Mb
Release : 2021-03-26
Category : Computers
ISBN : 9781351375108

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Concise Encyclopedia of Coding Theory by W. Cary Huffman,Jon-Lark Kim,Patrick Solé Pdf

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

Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 50,6 Mb
Release : 2008-01-08
Category : Mathematics
ISBN : 3540730516

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Combinatorial Algebraic Topology by Dimitry Kozlov Pdf

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Author : Michel Marie Deza,Elena Deza
Publisher : Springer
Page : 731 pages
File Size : 47,6 Mb
Release : 2014-10-08
Category : Mathematics
ISBN : 9783662443422

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Encyclopedia of Distances by Michel Marie Deza,Elena Deza Pdf

This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances. The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.

Author : Michael P Ryan Jr,Luis F Urrutia,Juan Carlos D'olivo,Federico Zertuche Mones,M Rosenbaum,Eduardo Nahmad-achar
Publisher : World Scientific
Page : 566 pages
File Size : 43,8 Mb
Release : 1991-08-12
Category : Electronic
ISBN : 9789814555951

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Relativity And Gravitation: Classical And Quantum - Proceedings Of The 7th Latin American Symposium On Relativity And Gravitation (Silarg Vii) by Michael P Ryan Jr,Luis F Urrutia,Juan Carlos D'olivo,Federico Zertuche Mones,M Rosenbaum,Eduardo Nahmad-achar Pdf

The Latin American Symposium on Relativity and Gravitation has been held every two or three years over the past twenty years. This is the seventh in the series.

Author : W. Cary Huffman,Vera Pless
Publisher : Cambridge University Press
Page : 668 pages
File Size : 49,5 Mb
Release : 2010-02-18
Category : Technology & Engineering
ISBN : 9781139439503

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Fundamentals of Error-Correcting Codes by W. Cary Huffman,Vera Pless Pdf

Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.