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.The 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.
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978-0-8218-0817-7 (9780821808177)
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Schweitzer Klassifikation
Computing composed products of polynomials by J. V. Brawley, S. Gao, and D. Mills Actions of linearized polynomials on the algebraic closure of a finite field by S. D. Cohen and D. Hachenberger On degree bounds for invariant rings of finite groups over finite fields by P. Fleischmann and W. Lempken Irreducible polynomials of given forms by S. Gao, J. Howell, and D. Panario An application of Galois calculus to $\mathbb {F}_t[t]$ by Y. Hellegouarch Composition behavior of sub-linearised polynomials over a finite field by M. Henderson and R. Matthews Kernels and defaults by P. Langevin and P. Sole Global function fields with many rational places and their applications by H. Niederreiter and C. Xing Traces of roots of unity over prime fields by G. Stein The fermat curve in charcteristic $p$ by H. Stichtenoth Computing zeta functions over finite fields by D. Wan Cyclic alternant codes induced by an automorphism of a GRS code by T. P. Berger On Kerdock codes by C. Carlet Permutation group of the $q$-ary image of some $q^m$-ary cyclic codes by J. Lacan and E. Delpeyroux The number of solutions to a system of equations and spectra of codes by O. Keren and S. Litsyn The LD probable prime test by W. More Carmichael numbers and Lucas tests by S. M. S. Muller On the state complexity of some long codes by T. Blackmore and G. Norton ID-based key distribution system over an elliptic curve by H. Sakazaki, E. Okamoto, and M. Mambo Symmetric sets of curves and combinatorial arrays by R. Fuji-Hara and S. Shinohara Weight functions and the extension theorem for linear codes over finite rings by J. A. Wood.
