|Universiteit Faculteit FNWI English version||24 september 2008, e-mail|
Woensdag 26 november 2008
AbstractLet q = pr be a prime power, and let f(x) = xm - fm-1xm-1 - ... - f1x - f0 be an irreducible polynomial over the finite field GF(q) of size q. A zero &xi of f is called nonstandard if the recurrence relation
In this talk, we first show that this classification problem is related to the problem of determining which cyclic codes over GF(q) possess extra permutation automorphisms.
Then we describe two classes of examples of nonstandard finite field elements.
Finally, we use the known classification of the subgroups of PGL(2,q) and a new result by Brison and Nogueira to show that these examples exhaust all possibilities in the case where m=2.