Finite Fields and Their Applications - Character Sums and Polynomials

Pascale Charpin (1) , Alexander Pott (2) , Arne Winterhof (3)

1 SECRET - Security, Cryptology and Transmissions
2 OVGU - Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University [Magdeburg]
3 RICAM - Johann Radon Institute for Computational and Applied Mathematics

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, Alexander Pott, Arne Winterhof (Dir.). Finite Fields and Their Applications - Character Sums and Polynomials. Pascale Charpin and Alexander Pott and Arne Winterhof. De Gruyter, 11, pp.274, 2013, Radon Series on Computational and applied mathematics, 978-3-11-028360-0. ⟨hal-00931614⟩