Çoban, Mustafa
(2003)
*Primitive elements in finite fields with arbitrary trace.*
[Thesis]

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## Abstract

Arithmetic of finite fields is not only important for other branches of mathematics but also widely used in applications such as coding and cryptography. A primitive element of a finite field is of particular interest since it enables one to represent all other elements of the field. Therefore an extensive research has been done on primitive elements, especially those satisfying extra conditions. We are interested in the existence of primitive elements in extensions of finite fields with prescribed trace value. This existence problem can be settled by means of two important theories. One is character sums and the other is the theory of algebraic function fields. The aim of this thesis is to introduce some important properties of these two topics and to show how they are used in answering the existence problem mentioned above.

Item Type: | Thesis |
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Uncontrolled Keywords: | Finite field, primitive element, trace, character sum, algebraic function field |

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: | 17 Apr 2008 15:38 |

Last Modified: | 26 Apr 2022 09:42 |

URI: | https://research.sabanciuniv.edu/id/eprint/8174 |