Dynamical Families of Quadratic Polynomials in Finite Fields of Characteristic Two
Eric Bach, Andrew Bridy · arXiv (Cornell University) · 2012
Let k be a finite field of even order. Let f in k[x] be a quadratic polynomial map from k to k. We show that f is conjugate by a linear polynomial in k[x] to a map in one of two one-parameter families. We then show that the number of equivalence classes of these f under conjugation by any permutation of k is 2^{O(n/(log log n))}. In doing do we prove a more general result about affine-linear maps on finite dimensional vector spaces over finite fields.