Arne Winterhof

Alexander Pott

Pascale Charpin

Character Sums and Polynomials

Finite Fields and Their Applications

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.

Claude Carlet

This book constitutes the proceedings of the 6th International Conference on Sequences and Their Applications held in Paris, France, in September 2010.

6th International Conference, Paris, France, September 13-17, 2010. Proceedings

Sequences and Their Applications - SETA 2010

 Gohar Kyureghyan

 Gary L. Mullen

This volume contains the proceedings of the 11th International Conference on Finite Fields and their Applications (Fq11), held July 22-26, 2013, in Magdeburg, Germany. Finite Fields are fundamental structures in mathematics. They lead to interesting deep problems in number theory, play a major role in combinatorics and finite geometry, and have a vast amount of applications in computer science. Papers in this volume cover these aspects of finite fields as well as applications in coding theory and cryptography.

Topics in Finite Fields

Solomon W. Golomb

Matthew G. Parker

This volume contains the refereed proceedings papers of the Fifth International ConferenceonSequencesandtheirApplications(SETA2008), heldinLexington, Kentucky (USA), September 14-18, 2008. The conference SETA is well est- lished in the mathematics and computer science community. Topics of "SETA" include - Randomness of sequences - Correlation (periodic and aperiodic types) and combinatorial aspects of - quences (di?erence sets) - Sequences with applications in coding theory and cryptography - Sequences over ?nite ?elds/rings/function ?elds - Linear and nonlinear feedback shift register sequences - Sequences for radar distance ranging, synchronization, identi?cation, and hardware testing - Sequences for wireless communication - Pseudorandom sequence generators - Correlation and transformation of Boolean functions - Multidimensional sequences and their correlation properties - Linear and nonlinear complexity of sequences. This year's proceedings contain 32 contributed papers. All papers have been thoroughly refereed by at least two referees. Most of the refereeing was done by members of the program committee. We thank all of them for their help. We arealsogratefultoSerdarBozta, s, Nina Brandst] atter, Nicolas Courtois, Fa- wei Fu, Honggang Hu, Alexander Kholosha, Emmanuel Prou?, Martin Ro ]tteler, Ayineedi Venkateswarlu and Bo-Yin Yang for their assistance in the reviewing process. In addition to the contributed papers, we had four invited lectures given by Claude Carlet (University of Paris 8, France), Pierre L'Ecuyer (Universit ́ede Montr ́ eal, Canada), Guang Gong (University of Waterloo, Canada) and Robert McEliece (California Institute of Technology, USA). You ?nd papers based on these invited talks in this volume.

Alexander Pott

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