LINEARIZED POLYNOMIALS OVER FINITE FIELDS

Leyla PARLAR

Mathematics, Master Thesis, 2012

 Thesis Jury

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

Place: 2008

Keywords: Linearized polynomials, permutation polynomials, p-to-1 mappings

Abstract

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.