**Contemporary Mathematics**

Volume: 225;
1999;
243 pp;
Softcover

MSC: Primary 11;
Secondary 05; 94

**Print ISBN: 978-0-8218-0817-7
Product Code: CONM/225**

List Price: $67.00

AMS Member Price: $53.60

MAA Member Price: $60.30

**Electronic ISBN: 978-0-8218-7816-3
Product Code: CONM/225.E**

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

# Finite Fields: Theory, Applications and Algorithms

Share this page *Edited by *
*Ronald C. Mullin; Gary L. Mullen*

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 up-to-date results from leading experts in the field.

#### Readership

Graduate students, pure and applied mathematicians, computer scientists, and communications engineers working in error-correcting codes and public key cryptography.

# Table of Contents

## Finite Fields: Theory, Applications and Algorithms

- Contents vii8 free
- Preface ix10 free
- Computing composed products of polynomials 112 free
- Actions of linearized polynomials on the algebraic closure of a finite field 1728
- On degree bounds for invariant rings of finite groups over finite fields 3344
- Irreducible polynomials of given forms 4354
- An application of Galois calculus to Fq[t] 5566
- Composition behavior of sub-linearised polynomials over a finite field 6778
- Kernels and defaults 7788
- Global function fields with many rational places and their applications 8798
- Traces of roots of unity over prime fields 113124
- The Fermat curve in characteristic p 123134
- Computing zeta functions over finite fields 131142
- Cyclic alternant codes induced by an automorphism of a GRS code 143154
- On Kerdock codes 155166
- Permutation group of the q-ary image of some qm-ary cyclic codes 165176
- The number of solutions to a system of equations and spectra of codes 177188
- The LD probable prime test 185196
- Carmichael numbers and Lucas tests 193204
- On the state complexity of some long codes 203214
- ID-based key distribution system over an elliptic curve 215226
- Symmetric sets of curves and combinatorial arrays 225236
- Weight functions and the extension theorem for linear codes over finite rings 231242