Hyperbolic geometry meets Coding theory: constellations and codes associated to Fuchsian groups

2016. 05. 10. 10:30
Prof. Montserrat Alsina (UPC)
The aim of the talk is to review the construction of fuchsian codes derived from orders in inde nite quaternion algebras and the associated fuchsian groups, published in recent papers as a joint work with I. Blanco-Chacon, C. Hollanti and D. Remon. Explicit examples allow to show how hyperbolic fundamental domains of fuchsian groups and the associated hyperbolic tessellations play an important role in the performance of these codes.
In this direction, we discuss why a careful study of centers of hyperbolic polygons would lead us to obtain properties on the codes, inorder to design better transmission schemes.