Finite Fields and Their Applications

Character Sums and Polynomials

Pascale Charpin, Alexander Pott, Arne Winterhof (Herausgeber)

Media-Kombination

XI, 274 Seiten | Ausstattung: eBook & Hardcover

2013
De Gruyter
9783110283617 (ISBN)

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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.

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.

Reihe/Serie	Radon Series on Computational and Applied Mathematics ; 11
Co-Autor	Guang Gong, Katalin Gyarmati, Fernando Hernando, Sophie Huczynska, Dieter Jungnickel, Gohar M. Kyureghyan, Gary Mcguire, Harald Niederreiter, Alina Ostafe, Igor E. Shparlinski
Zusatzinfo	Includes a print version and an ebook
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Almost perfect nonlinear function • Character sum • Exponential sum • finite field • Finite Field; Character Sum; Polynomial • Permutation Polynomial • polynomial
ISBN-13	9783110283617 / 9783110283617
Zustand	Neuware