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Finite Fields and Their Applications

Character Sums and Polynomials

Ed. by Charpin, Pascale / Pott, Alexander / Winterhof, Arne

With contrib. by Gong, Guang / Gyarmati, Katalin / Hernando, Fernando / Huczynska, Sophie / Jungnickel, Dieter / Kyureghyan, Gohar M. / McGuire, Gary / Niederreiter, Harald / Ostafe, Alina / Shparlinski, Igor E.

Series:Radon Series on Computational and Applied Mathematics 11

    139,95 € / $196.00 / £126.99*

    eBook (PDF)
    Publication Date:
    May 2013
    Copyright year:
    2013
    ISBN
    978-3-11-028360-0
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    Overview

    Aims and Scope

    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.

    Supplementary Information

    Details

    xi, 274 pages
    Language:
    English
    Type of Publication:
    Collection
    Keyword(s):
    Finite Field; Character Sum; Polynomial

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    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.

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