Codes From Difference Sets

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Codes From Difference Sets

Author : Cunsheng Ding
Publisher : World Scientific
ISBN 13 : 981461937X
Total Pages : 354 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Codes From Difference Sets by : Cunsheng Ding

Download or read book Codes From Difference Sets written by Cunsheng Ding and published by World Scientific. This book was released on 2014-08-08 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.

Difference Sets, Sequences and their Correlation Properties

Author : A. Pott
Publisher : Springer Science & Business Media
ISBN 13 : 9401144591
Total Pages : 451 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Difference Sets, Sequences and their Correlation Properties by : A. Pott

Download or read book Difference Sets, Sequences and their Correlation Properties written by A. Pott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: The explanation of the formal duality of Kerdock and Preparata codes is one of the outstanding results in the field of applied algebra in the last few years. This result is related to the discovery of large sets of quad riphase sequences over Z4 whose correlation properties are better than those of the best binary sequences. Moreover, the correlation properties of sequences are closely related to difference properties of certain sets in (cyclic) groups. It is the purpose of this book to illustrate the connection between these three topics. Most articles grew out of lectures given at the NATO Ad vanced Study Institute on "Difference sets, sequences and their correlation properties". This workshop took place in Bad Windsheim (Germany) in August 1998. The editors thank the NATO Scientific Affairs Division for the generous support of this workshop. Without this support, the present collection of articles would not have been realized.

Digital Broadcasting

Author : Tadashi Shiomi
Publisher : IOS Press
ISBN 13 : 9781586030995
Total Pages : 306 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Digital Broadcasting by : Tadashi Shiomi

Download or read book Digital Broadcasting written by Tadashi Shiomi and published by IOS Press. This book was released on 2000 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broadcast television began in Japan in 1953. Since then the presence of television has continued to grow and TV broadcasts are the most familiar source of information for most people. This book compiles the fundamentals of digital broadcast, which has developed since the advent of text caption broadcasting in 1985, it also looks at other advanced technology including terestrial broadcast, satellite broadcast and CATV - cable television.

New Advances in Designs, Codes and Cryptography

Author : Charles J. Colbourn
Publisher : Springer Nature
ISBN 13 : 303148679X
Total Pages : 442 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis New Advances in Designs, Codes and Cryptography by : Charles J. Colbourn

Download or read book New Advances in Designs, Codes and Cryptography written by Charles J. Colbourn and published by Springer Nature. This book was released on with total page 442 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.

Codes and Designs

Author : K. T. Arasu
Publisher : Walter de Gruyter
ISBN 13 : 3110198118
Total Pages : 333 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Codes and Designs by : K. T. Arasu

Download or read book Codes and Designs written by K. T. Arasu and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following an initiative of the late Hans Zassenhaus in 1965, the Departments of Mathematics at The Ohio State University and Denison University organize conferences in combinatorics, group theory, and ring theory. Between May 18-21, 2000, the 25th conference of this series was held. Usually, there are twenty to thirty invited 20-minute talks in each of the three main areas. However, at the 2000 meeting, the combinatorics part of the conference was extended, to honor the 65th birthday of Professor Dijen Ray-Chaudhuri. This volulme is the proceedings of this extension. Most of the papers are in coding theory and design theory, reflecting the major interest of Professor Ray-Chaudhuri, but there are articles on association schemes, algebraic graph theory, combinatorial geometry, and network flows as well. There are four surveys and seventeen research articles, and all of these went through a thorough refereeing process. The volume is primarily recommended for researchers and graduate students interested in new developments in coding theory and design theory.

Algebraic Coding Theory (Revised Edition)

Author : Elwyn R Berlekamp
Publisher : World Scientific
ISBN 13 : 981463591X
Total Pages : 501 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Algebraic Coding Theory (Revised Edition) by : Elwyn R Berlekamp

Download or read book Algebraic Coding Theory (Revised Edition) written by Elwyn R Berlekamp and published by World Scientific. This book was released on 2015-03-26 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.

Geometry, Combinatorial Designs and Related Structures

Author : J. W. P. Hirschfeld
Publisher : Cambridge University Press
ISBN 13 : 052159538X
Total Pages : 269 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Geometry, Combinatorial Designs and Related Structures by : J. W. P. Hirschfeld

Download or read book Geometry, Combinatorial Designs and Related Structures written by J. W. P. Hirschfeld and published by Cambridge University Press. This book was released on 1997-08-14 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines state of the art research in finite geometries and designs.

Groups, Difference Sets, and the Monster

Author : K. T. Arasu
Publisher : Walter de Gruyter
ISBN 13 : 9783110147919
Total Pages : 480 pages
Book Rating : 4.1/5 (479 download)

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Book Synopsis Groups, Difference Sets, and the Monster by : K. T. Arasu

Download or read book Groups, Difference Sets, and the Monster written by K. T. Arasu and published by Walter de Gruyter. This book was released on 1996 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Groups, Difference Sets, and the Monster".

Designs and Their Codes

Author : E. F. Assmus
Publisher : Cambridge University Press
ISBN 13 : 9780521458399
Total Pages : 366 pages
Book Rating : 4.4/5 (583 download)

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Book Synopsis Designs and Their Codes by : E. F. Assmus

Download or read book Designs and Their Codes written by E. F. Assmus and published by Cambridge University Press. This book was released on 1994-01-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.

Algebra

Author : I.B.S. Passi
Publisher : Birkhäuser
ISBN 13 : 3034899963
Total Pages : 247 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Algebra by : I.B.S. Passi

Download or read book Algebra written by I.B.S. Passi and published by Birkhäuser. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Indian National. Science Academy has planned to bring out monographs on special topics with the aim of providing acce~sible surveys/reviews of topics of current research in various fields. Prof. S.K. Malik, FNA, Editor of Publications INSA asked me in October 1997 to edit a volume on algebra in this series. I invited a number of algebraists, several of them working in group rings, and it is with great satisfaction and sincere thanks to the authors that I present here in Algebra: Some Recent Advances the sixteen contributions received in response to my invitations. I.B.S. Passi On Abelian Difference Sets K. r Arasu* and Surinder K. Sehgal 1. Introduction We review some existence and nonexistence results - new and old - on abelian difference sets. Recent surveys on difference sets can be found in Arasu (1990), Jungnickel (1992a, b), Pott (1995), Jungnickel and Schmidt (1997), and Davis and Jedwab (1996). Standard references for difference sets are Baumert (1971), Beth et al. (1998), and Lander (1983). This article presents a flavour of the subject, by discussing some selected topics. Difference sets are very important in combinatorial design theory and in commu nication engineering while designing sequences with good correlation properties. Our extended bibliography covers a wide variety of papers written in the area of difference sets and related topics.

Characters and Cyclotomic Fields in Finite Geometry

Author : Bernhard Schmidt
Publisher : Springer
ISBN 13 : 3540457976
Total Pages : 112 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Characters and Cyclotomic Fields in Finite Geometry by : Bernhard Schmidt

Download or read book Characters and Cyclotomic Fields in Finite Geometry written by Bernhard Schmidt and published by Springer. This book was released on 2004-10-13 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13

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 2024-02-29 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

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.

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.

An Introduction to Algebraic and Combinatorial Coding Theory

Author : Ian F. Blake
Publisher : Academic Press
ISBN 13 : 1483260291
Total Pages : 244 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis An Introduction to Algebraic and Combinatorial Coding Theory by : Ian F. Blake

Download or read book An Introduction to Algebraic and Combinatorial Coding Theory written by Ian F. Blake and published by Academic Press. This book was released on 2014-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Difference Sets

Author : Emily H. Moore
Publisher : American Mathematical Soc.
ISBN 13 : 0821891766
Total Pages : 315 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Difference Sets by : Emily H. Moore

Download or read book Difference Sets written by Emily H. Moore and published by American Mathematical Soc.. This book was released on 2013-06-13 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of f