Lower bounds for the minimum distance of algebraic geometry codes

A one-point AG-code is an algebraic geometry code based on a divisor whose support consists of one point. Since the discovery of the Feng-Rao lower bound for the minimum distance, there has been a renewed interest in such codes. This lower bound is also called the order bound. An alternative description of these codes in terms of order domains has been found.

In my talk I will indicate how one can use the ideas behind the order bound to obtain a lower bound for the minimum distance of any AG-code. After this I will compare this generalized order bound with other known lower bounds, such as the Goppa bound, the Feng-Rao bound and the Kirfel-Pellikaan bound.

I will finish my talk by giving several examples. Especially for two-point codes, the generalized order bound is fairly easy to compute. As an illustration, I will indicate how a lower bound can be obtained for the minimum distance of some two-point codes coming from the Hermitian curve and compare the outcome with some recent results of Kim and Homma.