On algebraic geometric codes and some related codes

Guenda, Kenza (2006-12)

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/2033
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