Bounds for generalized Hamming weights of general AG codes

We present a good bound for the generalized Hamming weights of multi-point evaluation and differential AG codes. It is a natural generalization of the order bound for one-point AG codes. As an example, we determine the third generalized Hamming weight of one particular two-point evaluation Hermitian code. Then we extend the bound for the relative generalized Hamming weights, which are essential measures of the performance of secret sharing schemes based on linear codes. The access structure of one particular secret sharing scheme based on the previous two-point Hermitian code and its subcode is analyzed using the new bound.