On algebraic geometric codes and some related codes
Date
2006-12
Authors
Guenda, Kenza
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
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.
Description
Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.
Keywords
Algebraic geometric codes, Error probability, BCH codes, List decoding, Dissertations -- Mathematics, Theses -- Mathematics, Geometry, Algebraic, Goppa codes, Reed-Solomon codes