Thesis (MSc (Mathematics))--University of Stellenbosch, 2006. / The main topic of this thesis is the construction of the algebraic geometric
codes (Goppa codes), and their decoding by the list-decoding, which allows
one to correct beyond half of the minimum distance. We also consider the
list-decoding of the Reed–Solomon codes as they are subclass of the Goppa
codes, and the determination of the parameters of the non primitive BCH
codes.
AMS Subject Classification: 4B05, 94B15, 94B35, 94B27, 11T71, 94B65,B70.
Keywords: Linear codes, cyclic codes, BCH codes, Reed–Solomon codes,
list-decoding, Algebraic Geometric codes, decoding, bound on codes, error
probability.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/2033 |
| Date | 12 1900 |
| Creators | Guenda, Kenza |
| Contributors | Green, Barry W., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | University of Stellenbosch |
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