Finite Fields and Their Applications

Published by De Gruyter 2013

Finite Fields and Their Applications

Character Sums and Polynomials

With contributions by: Guang Gong, Katalin Gyarmati, Fernando Hernando, Sophie Huczynska, Dieter Jungnickel, Gohar M. Kyureghyan, Gary McGuire, Harald Niederreiter, Alina Ostafe and Igor E. Shparlinski
Edited by: Pascale Charpin, Alexander Pott and Arne Winterhof

Volume 11 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110283600

Overview
Contents

About this book

This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012.

Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas:

Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums.
Chapters 3, 5, and 6 deal with polynomials over finite fields.
Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively.
Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation.
Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived.

The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.

Author information

Pascale Charpin, INRIA, Le Chesnay, France;Alexander Pott, Otto-von-Guericke-University Magdeburg, Germany; Arne Winterhof, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria.

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	vii
Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity Guang Gong Requires Authentication Unlicensed Licensed Download PDF	1
Measures of Pseudorandomness Katalin Gyarmati Requires Authentication Unlicensed Licensed Download PDF	43
Existence Results for Finite Field Polynomials with Specified Properties Sophie Huczynska Requires Authentication Unlicensed Licensed Download PDF	65
Incidence Structures, Codes, and Galois Geometries Dieter Jungnickel Requires Authentication Unlicensed Licensed Download PDF	89
Special Mappings of Finite Fields Gohar M. Kyureghyan Requires Authentication Unlicensed Licensed Download PDF	117
On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions Fernando Hernando and Gary McGuire Requires Authentication Unlicensed Licensed Download PDF	145
Finite Fields and Quasirandom Points Harald Niederreiter Requires Authentication Unlicensed Licensed Download PDF	169
Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects Alina Ostafe Requires Authentication Unlicensed Licensed Download PDF	197
Additive Combinatorics over Finite Fields: New Results and Applications Igor E. Shparlinski Requires Authentication Unlicensed Licensed Download PDF	233
Index Requires Authentication Unlicensed Licensed Download PDF	273
Backmatter Requires Authentication Unlicensed Licensed Download PDF	275

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers, Lecturers, and Graduate Students in Mathematics, e.g. Algebra, Number Theory, Cryptography, Coding Theory, Discrete Mathematics, Quasi-Monte Carlo Methods, Quantum Information Theory, Wireless Communication, and Sequence Design; Academic Libraries
Pages
- Front matter: 11
- Main content: 274
Illustrations
- Tables: 15
Keywords: Finite Field; Character Sum; Polynomial

eBook

Published: May 28, 2013
ISBN: 9783110283600

Hardcover

Published: May 21, 2013
ISBN: 9783110282405