Title: Computational aspects of algebraic geometry codes.
Abstract: In this talk, we present an overview over multiple computational
results related to algebraic geometry codes. In particular, we consider
encoding of one-point codes over a special family of curves called
$C_{ab}$-curves, which includes the famous Hermitian curve. In this setting,
we take advantage of the fact that encoding problem can be reduced to the
problem multi-point evaluation of bivariate polynomials, which we address in
two fundamentally different ways. In the final part of the talk, we will briefly
outline an efficient list decoding algorithm for general algebraic geometry codes.
The talk is based on results produced during the PhD studies of the speaker
under the supervision of J. Rosenkilde and P. Beelen.
