Posted by: atri | September 17, 2007

Project 1: Algebraic Geometric Codes

In class today I mentioned that the Shannon’s capacity theorem is proved using random codes. This is going to be recurring theme: almost always the best parameters are achieved by random codes. One notable exception is a specific class of codes called algebraic geometric codes which have better distance than random codes (for $q\ge 49$).

For a gentle introduction consult the notes from Sudan‘s course on coding theory. A more detailed exposition can be found in the chapter on Algebraic geometric codes by Høholdt, van Lint and Pellikaan (in Handbook of Coding theory, Eds: Pless, Huffman and Brualdi).

This project can be done jointly by two students. Warning: Algebraic geometric codes is based on some deep (and difficult) math so do not take on this project lightly.