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Product Code:  CONM/225 
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Book DetailsContemporary MathematicsVolume: 225; 1999; 243 ppMSC: Primary 11; Secondary 05; 94
The Fourth International Conference on "Finite Fields: Theory, Applications, and Algorithms" was held at the University of Waterloo in August 1997. This volume presents the refereed proceedings.
Because of its applications in so many diverse areas, finite fields continues to grow in importance in modern mathematics. Finite fields now play particularly important roles in number theory, algebra, and algebraic geometry. They also play a crucial role in computer science, statistics, and engineering. Areas of application include but are not limited to algebraic coding theory, cryptology, and combinatorial design theory. Computational and algorithmic aspects of finite field problems are also growing in significance.
The conference drew workers in theoretical, applied, and algorithmic finite field theory. All papers were refereed. They are loosely classified as theoretical and applied and are listed under these general headings. The work contains uptodate results from leading experts in the field.
ReadershipGraduate students, pure and applied mathematicians, computer scientists, and communications engineers working in errorcorrecting codes and public key cryptography.

Table of Contents

Articles

Joel V. Brawley, Shuhong Gao and Donald Mills — Computing composed products of polynomials [ MR 1650621 ]

Stephen D. Cohen and Dirk Hachenberger — Actions of linearized polynomials on the algebraic closure of a finite field [ MR 1650613 ]

Peter Fleischmann and Wolfgang Lempken — On degree bounds for invariant rings of finite groups over finite fields [ MR 1650609 ]

Shuhong Gao, Jason Howell and Daniel Panario — Irreducible polynomials of given forms [ MR 1650605 ]

Yves Hellegouarch — An application of Galois calculus to ${\bf F}_q[t]$ [ MR 1650601 ]

Marie Henderson and Rex Matthews — Composition behaviour of sublinearised polynomials over a finite field [ MR 1650597 ]

Philippe Langevin and Patrick Solé — Kernels and defaults [ MR 1650593 ]

Harald Niederreiter and Chaoping Xing — Global function fields with many rational places and their applications [ MR 1650592 ]

Greg Stein — Traces of roots of unity over prime fields [ MR 1650596 ]

Henning Stichtenoth — The Fermat curve in characteristic $p$ [ MR 1650600 ]

Daqing Wan — Computing zeta functions over finite fields [ MR 1650604 ]

Thierry P. Berger — Cyclic alternant codes induced by an automorphism of a GRS code [ MR 1650608 ]

Claude Carlet — On Kerdock codes [ MR 1650612 ]

Jérôme Lacan and Emmanuelle Delpeyroux — Permutation group of the $q$ary image of some $q^m$ary cyclic codes [ MR 1650616 ]

Osnat Keren and Simon Litsyn — The number of solutions to a system of equations and spectra of codes [ MR 1650620 ]

Willi More — The LD probable prime test [ MR 1650624 ]

Siguna M. S. Müller — Carmichael numbers and Lucas tests [ MR 1650628 ]

Tim Blackmore and Graham Norton — On the state complexity of some long codes [ MR 1650632 ]

Hisao Sakazaki, Eiji Okamoto and Masahiro Mambo — IDbased key distribution system over an elliptic curve [ MR 1650636 ]

Ryoh FujiHara and Satoshi Shinohara — Symmetric sets of curves and combinatorial arrays [ MR 1650640 ]

Jay A. Wood — Weight functions and the extension theorem for linear codes over finite rings [ MR 1650644 ]


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The Fourth International Conference on "Finite Fields: Theory, Applications, and Algorithms" was held at the University of Waterloo in August 1997. This volume presents the refereed proceedings.
Because of its applications in so many diverse areas, finite fields continues to grow in importance in modern mathematics. Finite fields now play particularly important roles in number theory, algebra, and algebraic geometry. They also play a crucial role in computer science, statistics, and engineering. Areas of application include but are not limited to algebraic coding theory, cryptology, and combinatorial design theory. Computational and algorithmic aspects of finite field problems are also growing in significance.
The conference drew workers in theoretical, applied, and algorithmic finite field theory. All papers were refereed. They are loosely classified as theoretical and applied and are listed under these general headings. The work contains uptodate results from leading experts in the field.
Graduate students, pure and applied mathematicians, computer scientists, and communications engineers working in errorcorrecting codes and public key cryptography.

Articles

Joel V. Brawley, Shuhong Gao and Donald Mills — Computing composed products of polynomials [ MR 1650621 ]

Stephen D. Cohen and Dirk Hachenberger — Actions of linearized polynomials on the algebraic closure of a finite field [ MR 1650613 ]

Peter Fleischmann and Wolfgang Lempken — On degree bounds for invariant rings of finite groups over finite fields [ MR 1650609 ]

Shuhong Gao, Jason Howell and Daniel Panario — Irreducible polynomials of given forms [ MR 1650605 ]

Yves Hellegouarch — An application of Galois calculus to ${\bf F}_q[t]$ [ MR 1650601 ]

Marie Henderson and Rex Matthews — Composition behaviour of sublinearised polynomials over a finite field [ MR 1650597 ]

Philippe Langevin and Patrick Solé — Kernels and defaults [ MR 1650593 ]

Harald Niederreiter and Chaoping Xing — Global function fields with many rational places and their applications [ MR 1650592 ]

Greg Stein — Traces of roots of unity over prime fields [ MR 1650596 ]

Henning Stichtenoth — The Fermat curve in characteristic $p$ [ MR 1650600 ]

Daqing Wan — Computing zeta functions over finite fields [ MR 1650604 ]

Thierry P. Berger — Cyclic alternant codes induced by an automorphism of a GRS code [ MR 1650608 ]

Claude Carlet — On Kerdock codes [ MR 1650612 ]

Jérôme Lacan and Emmanuelle Delpeyroux — Permutation group of the $q$ary image of some $q^m$ary cyclic codes [ MR 1650616 ]

Osnat Keren and Simon Litsyn — The number of solutions to a system of equations and spectra of codes [ MR 1650620 ]

Willi More — The LD probable prime test [ MR 1650624 ]

Siguna M. S. Müller — Carmichael numbers and Lucas tests [ MR 1650628 ]

Tim Blackmore and Graham Norton — On the state complexity of some long codes [ MR 1650632 ]

Hisao Sakazaki, Eiji Okamoto and Masahiro Mambo — IDbased key distribution system over an elliptic curve [ MR 1650636 ]

Ryoh FujiHara and Satoshi Shinohara — Symmetric sets of curves and combinatorial arrays [ MR 1650640 ]

Jay A. Wood — Weight functions and the extension theorem for linear codes over finite rings [ MR 1650644 ]