On the Efficient Decoding of Algebraic-Geometric Codes

This talk is intended to give a survey on the existing literature on the decoding of algebraic-geometric codes. Although the motivation originally was to find an efficient decoding algorithm for algebraic-geometric codes, the latest results give algorithms which can be explained purely in terms of linear algebra. We will treat the following subjects: 1.The decoding problem2.Decoding by error location3.Decoding by error location of algebraic-geometric codes4.Majority coset decoding5.Decoding algebraic-geometric codes by solving the key equation6.Improvements of the complexity