Author : Emily H. Moore
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 12,51 MB
Release : 2013-06-13
Category : Mathematics
ISBN : 0821891766
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
Author : A. Pott
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 21,66 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401144591
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.
Author : Cunsheng Ding
Publisher : World Scientific
Page : 354 pages
File Size : 31,5 MB
Release : 2014-08-08
Category : Mathematics
ISBN : 981461937X
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.
Author : K.T. Arasu
Publisher : Walter de Gruyter
Page : 477 pages
File Size : 18,26 MB
Release : 2011-06-24
Category : Mathematics
ISBN : 311089310X
This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Author : Bernhard Schmidt
Publisher : Springer
Page : 112 pages
File Size : 43,67 MB
Release : 2004-10-13
Category : Mathematics
ISBN : 3540457976
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
Author : Leonard D. Baumert
Publisher : Springer
Page : 172 pages
File Size : 26,5 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540364536
Author : Thomas Beth
Publisher : Cambridge University Press
Page : 730 pages
File Size : 13,38 MB
Release : 1999-11-18
Category : Mathematics
ISBN : 9780521444323
This is the first volume of the second edition of the standard text on design theory.
Author : Yury J. Ionin
Publisher : Cambridge University Press
Page : 548 pages
File Size : 27,1 MB
Release : 2006-05-25
Category : Language Arts & Disciplines
ISBN : 9780521818339
The aim of this book is to provide a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. All researchers in combinatorial designs, coding theory, and finite geometries will find much of interest here, and this book can also serve as a text for an advanced course in combinatorial designs.
Author : Charles J. Colbourn
Publisher : CRC Press
Page : 778 pages
File Size : 33,37 MB
Release : 2010-12-12
Category : Mathematics
ISBN : 9781420049954
From experimental design to cryptography, this comprehensive, easy-to-access reference contains literally all the facts you need on combinatorial designs. It includes constructions of designs, existence results, and properties of designs. Organized into six main parts, the CRC Handbook of Combinatorial Designs covers:
Author : Richard Klima
Publisher : CRC Press
Page : 536 pages
File Size : 42,97 MB
Release : 2006-07-12
Category : Mathematics
ISBN : 9781584886105
Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields. Carefully integrating MapleTM and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems. New to the Second Edition Three new chapters on Vigenère ciphers, the Advanced Encryption Standard (AES), and graph theory as well as new MATLAB and Maple sections Expanded exercises and additional research exercises Maple and MATLAB files and functions available for download online and from a CD-ROM With the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists.
