On applications of algebraic function fields to codes

Warning The system is temporarily closed to updates for reporting purpose.

Özdemir, Mehmet (2004) On applications of algebraic function fields to codes. [Thesis]

[thumbnail of ozdemirmehmet.pdf] PDF
ozdemirmehmet.pdf

Download (379kB)

Abstract

The relation between algebraic function fields over finite fields and coding theory started with Goppa's important code construction, which is nowadays called geometric Goppa codes. He used Riemann-Roch spaces of divisors and degree one (rational) places of a function field to write codes with good parameters. Since Goppa's work, interaction between function fields and codes has been investigated extensively and further applications in coding theory have been found. The aim of this thesis is to describe two of these applications. The first is Goppas idea and its generalization by Xing-Niederreiter-Lam and Heydtmann using higher degree places of the function field. The second application is the use of number of rational places of a function field to estimate the minimum distance of cyclic codes. We give two examples of cyclic codes; binary Hamming and BCH codes.
Item Type: Thesis
Uncontrolled Keywords: Algebraic function field. -- Ceding theory. -- Geometric goppa code. -- Cyclic code
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: 16 Apr 2008 16:45
Last Modified: 26 Apr 2022 09:43
URI: https://research.sabanciuniv.edu/id/eprint/8227

Actions (login required)

View Item
View Item