Perfect Codes And Related Structures

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Perfect Codes And Related Structures

Author : Tuvi Etzion
Publisher : World Scientific
ISBN 13 : 981125589X
Total Pages : 436 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Perfect Codes And Related Structures by : Tuvi Etzion

Download or read book Perfect Codes And Related Structures written by Tuvi Etzion and published by World Scientific. This book was released on 2022-03-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we develop the theory of one of the most fascinating topics in coding theory, namely, perfect codes and related structures. Perfect codes are considered to be the most beautiful structure in coding theory, at least from the mathematical side. These codes are the largest ones with their given parameters. The book develops the theory of these codes in various metrics — Hamming, Johnson, Lee, Grassmann, as well as in other spaces and metrics. It also covers other related structures such as diameter perfect codes, quasi-perfect codes, mixed codes, tilings, combinatorial designs, and more. The goal is to give the aspects of all these codes, to derive bounds on their sizes, and present various constructions for these codes.The intention is to offer a different perspective for the area of perfect codes. For example, in many chapters there is a section devoted to diameter perfect codes. In these codes, anticodes are used instead of balls and these anticodes are related to intersecting families, an area that is part of extremal combinatorics. This is one example that shows how we direct our exposition in this book to both researchers in coding theory and mathematicians interested in combinatorics and extremal combinatorics. New perspectives for MDS codes, different from the classic ones, which lead to new directions of research on these codes are another example of how this book may appeal to both researchers in coding theory and mathematicians.The book can also be used as a textbook, either on basic course in combinatorial coding theory, or as an advance course in combinatorial coding theory.

Coding Theory

Author : Jacobus H. van Lint
Publisher : Springer
ISBN 13 : 3662207125
Total Pages : 145 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Coding Theory by : Jacobus H. van Lint

Download or read book Coding Theory written by Jacobus H. van Lint and published by Springer. This book was released on 2013-12-11 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Information Security, Coding Theory and Related Combinatorics

Author : Dean Crnković
Publisher : IOS Press
ISBN 13 : 1607506629
Total Pages : 460 pages
Book Rating : 4.6/5 (75 download)

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Book Synopsis Information Security, Coding Theory and Related Combinatorics by : Dean Crnković

Download or read book Information Security, Coding Theory and Related Combinatorics written by Dean Crnković and published by IOS Press. This book was released on 2011 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Published in cooperation with NATO Emerging Security Challenges Division"--T.p.

Introduction to Coding Theory

Author : J. H. van Lint
Publisher : Springer Science & Business Media
ISBN 13 : 3662079984
Total Pages : 181 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Introduction to Coding Theory by : J. H. van Lint

Download or read book Introduction to Coding Theory written by J. H. van Lint and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathe maticians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. So, it is not surprising that one more book on this subject now appears. However, a little more justification of the book are necessary. A few years ago it was and a little more history remarked at a meeting on coding theory that there was no book available an introductory course on coding theory (mainly which could be used for for mathematicians but also for students in engineering or computer science). The best known textbooks were either too old, too big, too technical, too much for specialists, etc. The final remark was that my Springer Lecture Notes (# 201) were slightly obsolete and out of print. Without realizing what I was getting into I announced that the statement was not true and proved this by showing several participants the book Inleiding in de Coderingstheorie, a little book based on the syllabus of a course given at the Mathematical Centre in Amsterdam in 1975 (M. C. Syllabus 31).

Sequences and the de Bruijn Graph

Author : Tuvi Etzion
Publisher : Elsevier
ISBN 13 : 0443135185
Total Pages : 484 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Sequences and the de Bruijn Graph by : Tuvi Etzion

Download or read book Sequences and the de Bruijn Graph written by Tuvi Etzion and published by Elsevier. This book was released on 2024-05-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The de Bruijn graph was defined in 1949 to enumerate the number of closed sequences where each n-tuple appears exactly once as a window in a sequence. Through the years, the graph and its sequences have found numerous applications – in space technology, wireless communication, cryptography, parallel computation, genome assembly, DNA storage, and microbiome research, among others. Sequences and the de Bruijn Graph: Properties, Constructions, and Applications explores the foundations of theoretical mathematical concepts and the important applications to computer science, electrical engineering, and bioinformatics. The book introduces the various concepts, ideas, and techniques associated with the use of the de Bruijn Graph, providing comprehensive coverage of sequence classification, one-dimensional and two-dimensional applications, graphs, interconnected networks, layouts, and embedded systems. Researchers, graduate students, professors, and professionals working in the fields of applied mathematics, electrical engineering, computer science and bioinformatics will find this book useful. Investigates computational and engineering applications associated with the de Bruijn graph, its sequences, and their generalization Explores one-dimensional and two-dimensional sequences with special properties and their various properties and applications Introduces the rich structure of the de Bruijn graph and its sequences, in both mathematical theory and its applications to computing and engineering problems

Discrete Mathematics and Applications

Author : Andrei M. Raigorodskii
Publisher : Springer Nature
ISBN 13 : 3030558576
Total Pages : 499 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Discrete Mathematics and Applications by : Andrei M. Raigorodskii

Download or read book Discrete Mathematics and Applications written by Andrei M. Raigorodskii and published by Springer Nature. This book was released on 2020-11-21 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in discrete mathematics are presented in this book with applications in theoretical mathematics and interdisciplinary research. Each chapter presents new methods and techniques by leading experts. Unifying interdisciplinary applications, problems, and approaches of discrete mathematics, this book connects topics in graph theory, combinatorics, number theory, cryptography, dynamical systems, finance, optimization, and game theory. Graduate students and researchers in optimization, mathematics, computer science, economics, and physics will find the wide range of interdisciplinary topics, methods, and applications covered in this book engaging and useful.

Progress in Cryptology - INDOCRYPT 2001

Author : C. Pandu Rangan
Publisher : Springer Science & Business Media
ISBN 13 : 3540430105
Total Pages : 363 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Progress in Cryptology - INDOCRYPT 2001 by : C. Pandu Rangan

Download or read book Progress in Cryptology - INDOCRYPT 2001 written by C. Pandu Rangan and published by Springer Science & Business Media. This book was released on 2001-12-05 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference in Cryptology in India, INDOCRYPT 2001, held in Chennai, India in December 2001. The 31 revised full papers presented together with an invited survey were carefully reviewed and selected from 77 submissions. The papers are organized in topical sections on hashing, algebraic schemes, elliptic curves, coding theory, applications, cryptanalysis, distributed cryptography, Boolean functions, digitial signatures, and shift registers.

Coding Theory and Design Theory

Author : Dijen Ray-Chaudhuri
Publisher : Springer Science & Business Media
ISBN 13 : 1461389941
Total Pages : 252 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Coding Theory and Design Theory by : Dijen Ray-Chaudhuri

Download or read book Coding Theory and Design Theory written by Dijen Ray-Chaudhuri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".

3rd International Castle Meeting on Coding Theory and Applications

Author : Joaquim Borges
Publisher : Univ. Autònoma de Barcelona
ISBN 13 : 8449026881
Total Pages : 289 pages
Book Rating : 4.4/5 (49 download)

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Book Synopsis 3rd International Castle Meeting on Coding Theory and Applications by : Joaquim Borges

Download or read book 3rd International Castle Meeting on Coding Theory and Applications written by Joaquim Borges and published by Univ. Autònoma de Barcelona. This book was released on 2011-09-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1999, a conference called International Meeting on Coding Theory and Cryptography took place at Mota Castle in Castilia (Spain). The conference had great acceptance within the community of coding theory and cryptography researchers. At that moment, and also nowadays, there are not many international workshops about these topics, at least if we compare with other mathematical and engineering subjects of research. Therefore, the general desire was to continue with more Castle Meetings. However, the following conference did not take place until 2008. In that case, the conference was called II International Castle Meeting on Coding Theory and Applications allowing more topics related to coding theory apart from cryptography. Such conference took place at Mota Castle again and the number of participants was similar to the previous edition. The present edition of the conference, called III International Castle Meeting on Coding Theory and Applications has been held at Cardona Castle in Catalonia (Spain). The number of communications has increased and a number of selected papers will be published in a special issue of the journal Designs, Codes and Cryptography. As in the previous editions, the conference has been of high level with notorious invited speakers and scientic committee members.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Serdar Boztas
Publisher : Springer
ISBN 13 : 3540456244
Total Pages : 411 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Serdar Boztas

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Serdar Boztas and published by Springer. This book was released on 2003-06-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The AAECC Symposia Series was started in 1983 by Alain Poli (Toulouse), who, together with R. Desq, D. Lazard, and P. Camion, organized the ?rst conference. Originally the acronym AAECC meant “Applied Algebra and Error-Correcting Codes”. Over the years its meaning has shifted to “Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes”, re?ecting the growing importance of complexity in both decoding algorithms and computational algebra. AAECC aims to encourage cross-fertilization between algebraic methods and their applications in computing and communications. The algebraic orientation is towards ?nite ?elds, complexity, polynomials, and graphs. The applications orientation is towards both theoretical and practical error-correction coding, and, since AAECC 13 (Hawaii, 1999), towards cryptography. AAECC was the ?rst symposium with papers connecting Gr ̈obner bases with E-C codes. The balance between theoretical and practical is intended to shift regularly; at AAECC-14 the focus was on the theoretical side. The main subjects covered were: – Codes: iterative decoding, decoding methods, block codes, code construction. – Codes and algebra: algebraic curves, Gr ̈obner bases, and AG codes. – Algebra: rings and ?elds, polynomials. – Codes and combinatorics: graphs and matrices, designs, arithmetic. – Cryptography. – Computational algebra: algebraic algorithms. – Sequences for communications.

Concise Encyclopedia of Coding Theory

Author : W. Cary Huffman
Publisher : CRC Press
ISBN 13 : 1351375105
Total Pages : 998 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman

Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman and published by CRC Press. This book was released on 2021-03-26 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Topics in Geometry, Coding Theory and Cryptography

Author : Arnaldo Garcia
Publisher : Springer Science & Business Media
ISBN 13 : 1402053347
Total Pages : 212 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Topics in Geometry, Coding Theory and Cryptography by : Arnaldo Garcia

Download or read book Topics in Geometry, Coding Theory and Cryptography written by Arnaldo Garcia and published by Springer Science & Business Media. This book was released on 2006-11-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

Algorithms and Complexity

Author : Vangelis Th. Paschos
Publisher : Springer
ISBN 13 : 3319181734
Total Pages : 443 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Algorithms and Complexity by : Vangelis Th. Paschos

Download or read book Algorithms and Complexity written by Vangelis Th. Paschos and published by Springer. This book was released on 2015-05-15 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 9th International Conference on Algorithms and Complexity, CIAC 2015, held in Paris, France, in May 2015. The 30 revised full papers presented were carefully reviewed and selected from 93 submissions and are presented together with 2 invited papers. The papers present original research in the theory and applications of algorithms and computational complexity.

Lattices Applied to Coding for Reliable and Secure Communications

Author : Sueli I.R. Costa
Publisher : Springer
ISBN 13 : 3319678825
Total Pages : 123 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Lattices Applied to Coding for Reliable and Secure Communications by : Sueli I.R. Costa

Download or read book Lattices Applied to Coding for Reliable and Secure Communications written by Sueli I.R. Costa and published by Springer. This book was released on 2018-04-02 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.

The Theory of Error Correcting Codes

Author : Florence Jessie MacWilliams
Publisher :
ISBN 13 :
Total Pages : 788 pages
Book Rating : 4.3/5 (91 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 1977 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lattices and Codes

Author : Wolfgang Ebeling
Publisher : Springer Science & Business Media
ISBN 13 : 3658003596
Total Pages : 177 pages
Book Rating : 4.6/5 (58 download)

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Book Synopsis Lattices and Codes by : Wolfgang Ebeling

Download or read book Lattices and Codes written by Wolfgang Ebeling and published by Springer Science & Business Media. This book was released on 2013 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated. Content Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes. Readership Graduate Students in Mathematics and Computer Science Mathematicians and Computer Scientists About the Author Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany

Handbook of Combinatorial Designs

Author : Charles J. Colbourn
Publisher : CRC Press
ISBN 13 : 1420010549
Total Pages : 1011 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Combinatorial Designs by : Charles J. Colbourn

Download or read book Handbook of Combinatorial Designs written by Charles J. Colbourn and published by CRC Press. This book was released on 2006-11-02 with total page 1011 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence