On irreducible binary polynomials

Official URL: http://192.168.1.20/record=b1378263 (Table of Contents)

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.