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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