Section: Scientific Foundations

Algebraic Geometry codes

There are many other applications of algorithmic methods for algebraic curves besides asymmetric cryptography. These algebraic geometry (AG) codes form a very powerful family of codes that often beat records for their parameters: they often offer the best correction capacity. The main topic of research is to accelerate the decoding algorithms of these codes, which have a slightly expensive cost [57] . A reference implementation would be of major interest, to help people compare AG codes with Reed–Solomon codes.

Guruswami and Sudan have obtained a breakthrough [55] for decoding AG codes with many errors. Still, there is no implementation available yet, even for the most simple AG codes (which are the Hermitian codes). In this domain too, the main problem is find a reasoneable complexity for these algorithms. implementation.