ON THE IRREDUCIBILITY OF SOME CLASSES OF POLYNOMIALS OVER FINITE FIELDS

Halime Ömrüuzun
Mathematics, MSc. Thesis, 2016

Thesis Jury

Prof. Dr. Alev Topuzoğlu(Thesis Advisor), Prof. Dr. Henning Stichtenoth, Asst. Prof. Dr. Seher Tutdere

Date & Time: August 4th, 2016 –  15:30 PM

Place: FENS 2008

Keywords : irreducible polynomials, divisibility, self-reciprocal polynomials, prescribed coefficient.

Abstract

In this thesis we focus on irreducibility of binomials and trinomials over finite fields Fq . After the introductory Chapter 1, we collect the well-known results in Chapter 2, where we also present the number of irreducible factors of a fixed degree k of a binomial, due to L. Redei. Chapter 3 is on self-reciprocal polynomials. An infinite family of irreducible, self-reciprocal polynomials over F2 is presented in Section 3.2. This family is obtained by J.L. Yucas and G.L. Mullen. Divisibility of self-reciprocal polynomials over F2 and F3 are studied in Sections 3.3 and 3.4. The last chapter aims to give a survey of recent results on various problems concerning irreducible polynomials with prescribed coefficients.