Cyclic Difference Sets


Book Description







Difference Sets, Sequences and their Correlation Properties


Book Description

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.




Difference Sets


Book Description

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




Codes From Difference Sets


Book Description

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.




Groups, Difference Sets, and the Monster


Book Description

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.




Algebraic Aspects of Digital Communications


Book Description

-Proceedings of the NATO Advanced Study Institute on New Challenges in Digital Communications, Vlora, Albania, 27 April - 9 May 2008.---T.p. verso.




Handbook of Combinatorial Designs


Book Description

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




Sequences and Their Applications -- SETA 2012


Book Description

This book constitutes the refereed proceedings of the 7th International Conference on Sequences and Their Applications, SETA 2012, held in Waterloo, Canada, in June 2012. The 28 full papers presented together with 2 invited papers in this volume were carefully reviewed and selected from 48 submissions. The papers are grouped in topical sections on perfect sequences; finite fields; boolean functions; Golomb 80th birthday session; linear complexity; frequency hopping; correlation of sequences; bounds on sequences, cryptography; aperiodic correlation; and Walsh transform.




CRC Handbook of Combinatorial Designs


Book Description

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: