LINEARIZED PoLYNOMIALS OVER FINITE FIELDS
Mathematics, Master Thesis, 2012
Prof. Dr. Henning Stichtenoth (Thesis Supervisor), Prof. Dr. Alev Topuzoğlu, Assoc. Prof. Cem Güneri, Assoc. Prof. Özgür Gürbüz, Asst. Prof. Kağan Kurşungöz,
Date & Time: May 30th 2012 – 09:30
Keywords: Linearized polynomials, permutation polynomials, p-to-1 mappings
We first study the ring of q-polynomials over the finite field with q elements by constructing an isomorphism between this ring and the polynomial ring over the finite field with q elements and by presenting several important facts about the polynomials in this ring. We also give characterizations for permutation polynomials of the finite field with p^n elements derived from p-polynomials over the finite field with p^n elements, based on a paper of P. Charpin and G. Kyureghyan. Furthermore, we present several results on q-polynomials over the finite field with q^n elements with kernel of any given dimension, following a paper by S. Ling and L.J. Qu.