On irreducible binary polynomials

Ongan, Pınar (2011) On irreducible binary polynomials. [Thesis]

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In the article [1], Michon and Ravache define a group action of S3 on the set of irreducible polynomials of degree ≥ 2 over F2, and seeing that the orbits can have 1, 2, 3, or 6 elements, they give answers to the following two questions: Which polynomials have i ∈ {1, 2, 3, 6} elements in their orbits? Within the orbits of the irreducible polynomials of degree n ≥ 2, how many of them consist of i ∈ {1, 2, 3, 6 } elements? After their article, the next step seems to generalize their results to the Fq-case, however, their de nition of the group action is not so suitable for such an extension. Therefore it is defined in a slightly different approach in this master thesis so that it can be easily generalized to the Fq-case later. Furthermore, the results of the article [1] are reacquired using the new definition. Additionally, in the light of the articles [2] by Meyn and [3] by Michon and Ravache, the construction of irreducible polynomials of a higher degree which remain invariant under the group action of a given element forms a part of this thesis.
Item Type: Thesis
Uncontrolled Keywords: Finite fields. -- Irreducible polynomials. -- Group actions. -- General linear group of degree two. -- Permutations. -- 2x2 invertible matrices. -- Sonlu cisimler. -- İndirgenemez polinomlar. -- Grup etkileri. -- 2x2 terslenebilir matrisler. -- Permütasyonlar.
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: 07 Jul 2014 01:18
Last Modified: 26 Apr 2022 10:01
URI: https://research.sabanciuniv.edu/id/eprint/24317

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