Danmarks Frie Forskningsfond (Independent Research Fund Denmark) each year supports many prestigious research projects. They have just announced that they will support a research project of the algebra group. This grant will enable us to hire a Ph.D. student as well as to visit and invite researchers from all over the world. We are very grateful for the support!
A brief summary of the research project is the following:
Error-correcting codes ensure reliability in e.g. satellite communication, distributed storage and cloud computing. It is vital that the error-correction can be done fast. Excellent error-correcting codes can be constructed using algebraic curves – AG codes – but no fast decoding algorithms are available for these codes. This has limited their theoretical impact and prohibited any practical impact. This project aims to change that.
Decoding of AG codes boils down to solving a Padé approximation on the algebraic curve. Current techniques throw away many levels of structure, leaving a problem on univariate polynomials. We will seek algorithms that retain these levels, and we will build on the latest developments in computer algebra. We expect improvements for both the simplest as well as more complex AG codes.
The project will be carried out by the algebra group at DTU and international collaborators from France and Canada.