Finite fields and their applications : character sums and polynomials / edited by Pascale Charpin, Alexander Pott, Arne Winterhof.

Format:

Book

Conference/Event

Contributor:

Charpin, P. (Pascale), 1949-

Pott, Alexander, 1961-

Winterhof, Arne.

Conference Name:

RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials (2012 : Strobl, Austria)

Series:

Radon series on computational and applied mathematics ; 11.

Radon series on computational and applied mathematics, 1865-3707 ; v. 11

Language:

English

Subjects (All):

Finite fields (Algebra)--Congresses.

Finite fields (Algebra).

Mathematics--Congresses.

Mathematics.

Telecommunication systems--Congresses.

Telecommunication systems.

Electronics--Congresses.

Electronics.

Physical Description:

1 online resource (288 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2013.

Language Note:

English

Summary:

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.

Contents:

Front matter

Preface

Contents

Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity / Gong, Guang

Measures of Pseudorandomness / Gyarmati, Katalin

Existence Results for Finite Field Polynomials with Specified Properties / Huczynska, Sophie

Incidence Structures, Codes, and Galois Geometries / Jungnickel, Dieter

Special Mappings of Finite Fields / Kyureghyan, Gohar M.

On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions / Hernando, Fernando / McGuire, Gary

Finite Fields and Quasirandom Points / Niederreiter, Harald

Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects / Ostafe, Alina

Additive Combinatorics over Finite Fields: New Results and Applications / Shparlinski, Igor E.

Index

Backmatter

Notes:

Based on the RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials, held at the Federal Institute for Adult Education in Strobl, Austria, September 2-7, 2012.

Includes bibliographical references and index.

CC BY-NC-ND

OCLC:

851970457