Title: Algebraic function fields, algebraic curves and Goppa codes
Other Titles: Algebraische Funktionenkörper, algebraische Kurven und Goppa Codes
Language: English
Authors: Kuleff, Peter Michael 
Qualification level: Diploma
Keywords: algebraische Funktionenkörper; algebraische Kurven; Goppa Codes
algebraic function field; algebraic curve; Goppa code
Advisor: Dorfer, Gerhard 
Issue Date: 2017
Number of Pages: 90
Qualification level: Diploma
This thesis gives an introduction into the theory of algebraic function fields and algebraic curves with an application to Goppa codes. The first two chapters focus on function fields in a purely algebraic setting and have the Riemann-Roch Theorem as their main result. Algebraic curves are approached from the perspective of function fields. Two kinds of Goppa codes are defined via places and local components of differentials, respectively. An example of how to construct Goppa codes from algebraic curves is given. In the last chapter a standard decoding scheme as well as a list decoding algorithm for Goppa codes are presented.
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-95610
Library ID: AC13642476
Organisation: E104 - Institut für Diskrete Mathematik und Geometrie 
Publication Type: Thesis
Appears in Collections:Thesis

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