On some classes of irreducible polynomials over finite fields

Ömrüuzun, Halime (2016) On some classes of irreducible polynomials over finite fields. [Thesis]

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In this thesis we describe the work in literature on various aspects of the theory of polynomials over nite elds. We focus on properties like irreducibility and divisibility. We also consider existence and enumeration problems for irreducible polynomials of special types. After the introductory Chapter 1, we collect the well-known results on irreducibility of binomials and trinomials in Chapter 2, where we also present the number of irreducible factors of a xed degree k of xt due to L. Redei. Chapter 3 is on self-reciprocal polynomials. An in nite family of irreducible, self-reciprocal polynomials over F2 is presented in Section 3.2. This family was obtained by J. L. Yucas and G. L. Mullen. Divisibility of self-reciprocal polynomials over F2 and F3 is studied in Sections 3.3 and 3.4 following the work of R. Kim and W. Koepf. The last chapter aims to give a survey of recent results concerning existence and enumeration of irreducible polynomials with prescribed coefficients.
Item Type: Thesis
Additional Information: Yükseköğretim Kurulu Tez Merkezi Tez No: 444564.
Uncontrolled Keywords: Irreducible polynomials. -- Divisibilit. -- Self-reciprocal polynomials. -- Prescribed coe cients. -- İndirgenemez polinomlar. -- Bölünebilirlik. -- Öz karşılıklı polinomlar. -- Saptanmış katsayılar.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 29 Apr 2018 14:26
Last Modified: 26 Apr 2022 10:19
URI: https://research.sabanciuniv.edu/id/eprint/34607

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