Seminar Coding Theory & Cryptography: Alberto Ravagnani
Alberto Ravagnani, University of Trento (Italy)
On Goppa codes on the Hermitian curve and its quotients
The dual minimum distance of two-point Goppa codes on the Hermitian curve has been determined by S. Park in 2010. The algebraic geometry of the curve can be used to explicitly describe the supports of the minimum-weight codewords of these codes and compute their number. A description of certain small-weight codewords can also be performed. Many plane curves covered by the Hermitian curve turn out to be useful in coding theory, even if they are singular curves. The minimum distance and the minimum-weight codewords of codes arising from these curves are essentially determined by the geometry of the normalization morphism.
Location: Grosser Hörsaal