This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.

This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.

This volume contains the refereed proceedings of the International Conference on Sequences and Their Applications which was held at the River View Ho- tel in Singapore during December 14-17, 1998. The program of this conference was arranged by a committee consisting of Claude Carlet (University of Caen) , Agnes Chan (Northeastern University), Cunsheng Ding (National University of Singapore, co-chair), Dieter Gollmann (Microsoft Research), Tor Helleseth (Uni- versity of Bergen, co-chair), Kyoki Imamura (Kyushu Institute of Technology), Andrew Klapper (University of Kentucky), Vijay Kumar (University of Southern California), Siu Lun Ma (National University of Singapore), Harald Niederreiter (A ustrian Academy of Sciences, co-chair), Dilip Sarwate (University of Illinois at Urbana-Champaign), Hans Schotten (Aachen University of Technology), Jeffrey Shallit (University of Waterloo), Neil Sloane (AT&T Shannon Lab), and Aimo Tietiivajnen (University of Turku). The local organization was in the hands of Cunsheng Ding, Kwok Van Lam (chair), Sjauntele Lau, and Sew Kiok Toh, all of the National University of Singapore. The idea for the conference grew out of the recognition that sequences in discrete structures like the ring of integers, residue class rings of the integers, and finite fields have found many important applications in modern information and communication technologies. Among these applications we mention cryp- tographic schemes, ranging systems, spread spectrum communication systems, multi-terminal system identification, code-division mUltiple-access communica- tion systems, global positioning systems, software testing, circuit testing, and computer simulation. There are also connections between sequences in discrete structures and error-correcting codes.

This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical ("a priori") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "random" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These "quasi-random" points are produced by deterministic algorithms and should be as "super" uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets."

Finite fields are algebraic structures in which there is much research interest and they have been shown to have a wide range of applications. These proceedings give a state-of-the-art account of the area of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. These also demonstrate inter-connections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.