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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.
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