Contemporary Mathematics 1999; 243 pp; softcover Volume: 225 ISBN10: 0821808176 ISBN13: 9780821808177 List Price: US$63 Member Price: US$50.40 Order Code: CONM/225
 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. Readership Graduate students, pure and applied mathematicians, computer scientists, and communications engineers working in errorcorrecting codes and public key cryptography. Table of Contents  J. V. Brawley, S. Gao, and D. Mills  Computing composed products of polynomials
 S. D. Cohen and D. Hachenberger  Actions of linearized polynomials on the algebraic closure of a finite field
 P. Fleischmann and W. Lempken  On degree bounds for invariant rings of finite groups over finite fields
 S. Gao, J. Howell, and D. Panario  Irreducible polynomials of given forms
 Y. Hellegouarch  An application of Galois calculus to \(\mathbb {F}_t[t]\)
 M. Henderson and R. Matthews  Composition behavior of sublinearised polynomials over a finite field
 P. Langevin and P. Solé  Kernels and defaults
 H. Niederreiter and C. Xing  Global function fields with many rational places and their applications
 G. Stein  Traces of roots of unity over prime fields
 H. Stichtenoth  The fermat curve in charcteristic \(p\)
 D. Wan  Computing zeta functions over finite fields
 T. P. Berger  Cyclic alternant codes induced by an automorphism of a GRS code
 C. Carlet  On Kerdock codes
 J. Lacan and E. Delpeyroux  Permutation group of the \(q\)ary image of some \(q^m\)ary cyclic codes
 O. Keren and S. Litsyn  The number of solutions to a system of equations and spectra of codes
 W. More  The LD probable prime test
 S. M. S. Müller  Carmichael numbers and Lucas tests
 T. Blackmore and G. Norton  On the state complexity of some long codes
 H. Sakazaki, E. Okamoto, and M. Mambo  IDbased key distribution system over an elliptic curve
 R. FujiHara and S. Shinohara  Symmetric sets of curves and combinatorial arrays
 J. A. Wood  Weight functions and the extension theorem for linear codes over finite rings
