ON THE IRREDUCIBILITY OF SOME CLASSES OF POLYNOMIALS OVER FINITE FIELDS
Mathematics, MSc. Thesis, 2016
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.
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.