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 problem 2. Decoding by error location 3. Decoding by error location of algebraic-geometric codes 4. Majority coset decoding 5. Decoding algebraic-geometric codes by solving the key equation 6. Improvements of the complexity

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