Finite Fields and Their Applications

Character Sums and Polynomials
1. Auflage 2013
ISBN: 978-3-11-028240-5
Verlag: De Gruyter

Buch, Englisch, Band 11, 274 Seiten, HC runder Rücken kaschiert, Format (B × H): 175 mm x 246 mm, Gewicht: 731 g

Reihe: ISSN

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.

Zielgruppe

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

Autoren/Hrsg.

Winterhof, Arne

Charpin, Pascale

Pott, Alexander

Weitere Mitwirkende

Gong, Guang

Gyarmati, Katalin

Hernando, Fernando

Huczynska, Sophie

Jungnickel, Dieter

Kyureghyan, Gohar M.

McGuire, Gary

Niederreiter, Harald

Ostafe, Alina

Shparlinski, Igor E.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Über Autor(innen)

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.