Codes From Difference Sets
Codes From Difference Sets

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

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.

Boolean Functions for Cryptography and Coding Theory
Boolean Functions for Cryptography and Coding Theory

Author: Claude Carlet

Publisher: Cambridge University Press

Published: 2021-01-07

Total Pages: 577

ISBN-13: 1108634664

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Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.

New Directions in Wireless Communications Research
New Directions in Wireless Communications Research

Author: Vahid Tarokh

Publisher: Springer Science & Business Media

Published: 2009-08-19

Total Pages: 483

ISBN-13: 1441906738

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New Directions in Wireless Communications Research addresses critical issues in the design and performance analysis of current and future wireless system design. Intended for use by system designers and academic researchers, the contributions are by acknowledged international leaders in their field. Topics covered include: (1) Characterization of wireless channels; (2) The principles and challenges of OFDM; (3) Low-correlation sequences for communications; (4) Resource allocation in wireless systems; (5) Signal processing for wireless systems, including iterative systems collaborative beamforming and interference rejection and network coding; (6) Multi-user and multiple input-multiple output (MIMO) communications; (7) Cooperative wireless networks, cognitive radio systems and coded bidirectional relaying in wireless networks; (8) Fourth generation standards such as LTE and WiMax and standard proposals such as UMB. With chapters from some of the leading researchers in the field, this book is an invaluable reference for those studying and practicing in the field of wireless communications. The book provides the most recent information on topics of current interest to the research community including topics such as sensor networks, coding for networks, cognitive networks and many more.

Computational and Algorithmic Problems in Finite Fields
Computational and Algorithmic Problems in Finite Fields

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 253

ISBN-13: 940111806X

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This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.

Arithmetic of Finite Fields
Arithmetic of Finite Fields

Author: Sihem Mesnager

Publisher: Springer Nature

Published: 2023-01-10

Total Pages: 353

ISBN-13: 3031229444

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This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2022, held in Chengdu, China, in August – September 2022. The 19 revised full papers and 3 invited talks presented were carefully reviewed and selected from 25 submissions. The papers are organized in topical sections: structures in finite fields; efficient finite field arithmetic; coding theory; cryptography; sequences.

Sequences and their Applications
Sequences and their Applications

Author: C. Ding

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 404

ISBN-13: 1447105516

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This book contains survey papers and research papers by leading experts on sequences and their applications. It discusses both the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation and computer simulation. Sequences have important applications in ranging systems, spread spectrum communication systems, multi-terminal system identification, code division multiply access communications systems, global positioning systems, software testing, circuit testing, computer simulation, and stream ciphers. The papers contained in this volume bring together experts from discrete mathematics, computer science and communications engineering, and help to bridge advances in these different areas.