On algebraic geometric codes and some related codes

[摘要] The main topic of this thesis is the construction of the algebraic geometriccodes (Goppa codes), and their decoding by the list-decoding, which allowsone to correct beyond half of the minimum distance. We also consider thelist-decoding of the Reed–Solomon codes as they are subclass of the Goppacodes, and the determination of the parameters of the non primitive BCHcodes.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, errorprobability.

[发布机构] Stellenbosch University