The minimum weights of two-point AG codes on norm-trace curves

We construct two-point algebraic geometry codes (AG codes) on algebraic curves over a finite field. We find the order-like bound on the minimum weights of these codes on algebraic curves, and we prove that this order-like bound is better than the Goppa bound. On norm-trace curves over the finite fields of characteristic 2, we explicitly determine the order-like bounds for one-point AG codes and two-point AG codes. Consequently, it turns out that the order-like bound for two-point AG codes on norm-trace curves is better than that of one-point codes on the same curves except for a few cases.