MSc. Thesis Defense:Halime Ömrüuzun
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  • MSc. Thesis Defense:Halime Ömrüuzun

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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.