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Geometry --- Difference sets --- Eindige meetkunden --- Ensembles de differences --- Finite geometries --- Fourier [Transformations de ] --- Fourier transformaties --- Fourier transformations --- Geometries finies --- Sets [Difference] --- Transformations [Fourier ] --- Transformations de Fourier --- Transforms [Fourier ] --- Verschilverzamelingen --- Verzamelingen [Verschil ] --- Difference sets. --- Finite geometries. --- Fourier transformations.

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Sequences (Mathematics) --- Coding theory --- Engineering & Applied Sciences --- Applied Mathematics --- Computer Science --- Mathematical sequences --- Numerical sequences --- Computer science. --- Computer communication systems. --- Data encryption (Computer science). --- Coding theory. --- Algorithms. --- Computer science --- Management information systems. --- Computer Science. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Data Encryption. --- Computer Communication Networks. --- Management of Computing and Information Systems. --- Coding and Information Theory. --- Mathematics. --- Computer-based information systems --- EIS (Information systems) --- Executive information systems --- MIS (Information systems) --- Sociotechnical systems --- Information resources management --- Management --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Algebra --- Arithmetic --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Cryptography --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Informatics --- Science --- Communication systems --- Mathematics --- Foundations --- Distributed processing --- Computational complexity. --- Computer software. --- Information Systems. --- Cryptology. --- Complexity, Computational --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Information theory. --- Communication theory --- Communication --- Cybernetics --- Paris <2010> --- Discrete mathematics. --- Cryptography. --- Computer networks. --- Electronic data processing—Management. --- IT Operations. --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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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.

Finite fields (Algebra) --- Mathematics --- Telecommunication systems --- Electronics --- Character Sum. --- Finite Field. --- Polynomial.

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This book constitutes the refereed proceedings of the 5th International Conference on Sequences and Their Applications, SETA 2008, held in Lexington, KY, USA in September 2008. The 32 revised full papers presented were carefully reviewed and selected. The papers are organized in topical sections on probabilistic methods and randomness properties of sequences; correlation; combinatorial and algebraic foundations; security aspects of sequences; algorithms; correlation of sequences over rings; nonlinear functions over finite fields.

Mathematical logic --- Algebra --- Ergodic theory. Information theory --- Complex analysis --- Discrete mathematics --- Computer science --- Computer architecture. Operating systems --- algebra --- coderen --- DES (data encryption standard) --- discrete wiskunde --- complexe analyse (wiskunde) --- informatica --- informatietheorie