Normal closure and Galois group of some field extension of F2 and good error correcting codes

Crane, Harry (2024) Normal closure and Galois group of some field extension of F2 and good error correcting codes. Bachelor's Thesis, Mathematics.

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Abstract

In a paper by Jaap Top, a certain tower of quadratic extensions of fields F2(x) \subset K_1\subset K_2\subset K_3\subset K_4 is constructed, with F2(x) denoting the field of rational functions over the field F2 of cardinality 2, and such that K_4 over K_1 is a Galois extension with Galois group Gal(K_4/K_1) isomorphic to Z/2Z x Z/2Z x Z/2Z. A goal of the present thesis is to show that the total extension K_4 over F2(x) is not Galois, and to describe the normal closure N of this extension and its Galois group over F2(x). Moreover, we consider intermediate fields and we use examples of those for constructing error correcting codes, as explained, for example, in Chapter 2 of H. Stichtenoth's textbook and in less detail at the end of this text.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Top, J.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	28 May 2024 09:35
Last Modified:	28 May 2024 09:35
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/32446

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