Codes from Difference Sets

Codes from Difference Sets PDF

Author: Cunsheng Ding

Publisher: World Scientific Publishing Company Incorporated

Published: 2014-08-08

Total Pages: 341

ISBN-13: 9789814619356

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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.

Codes From Difference Sets

Codes From Difference Sets PDF

Author: Cunsheng Ding

Publisher: World Scientific

Published: 2014-08-08

Total Pages: 354

ISBN-13: 981461937X

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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

Difference Sets, Sequences and their Correlation Properties PDF

Author: A. Pott

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 451

ISBN-13: 9401144591

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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.

Codes and Designs

Codes and Designs PDF

Author: K. T. Arasu

Publisher: Walter de Gruyter

Published: 2008-08-22

Total Pages: 333

ISBN-13: 3110198118

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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.

Combinatorics and Finite Fields

Combinatorics and Finite Fields PDF

Author: Kai-Uwe Schmidt

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-07-08

Total Pages: 354

ISBN-13: 3110642093

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Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.

Algebraic Coding Theory (Revised Edition)

Algebraic Coding Theory (Revised Edition) PDF

Author: Elwyn R Berlekamp

Publisher: World Scientific

Published: 2015-03-26

Total Pages: 501

ISBN-13: 981463591X

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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.

Difference Sets

Difference Sets PDF

Author: Emily H. Moore

Publisher: American Mathematical Soc.

Published: 2013-06-13

Total Pages: 315

ISBN-13: 0821891766

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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

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