1-2hit |
Hφholdt, van Lint and Pellikaan proposed a generalization of one-point AG codes, called the evaluation codes. We show that an evaluation code from a weight function can be constructed as Miura's generalization of one-point AG codes. Hence we can construct a one-point AG code as good as a given evaluation code from a weight function.
When we have a singular Cab curve with many rational points, we had better to construct linear codes on its normalization rather than the original curve. The only obstacle to construct linear codes on the normalization is finding a basis of L( Q) having pairwise distinct pole orders at Q, where Q is the unique place of the Cab curve at infinity. We present an algorithm finding such a basis from defining equations of the normalization of the original Cab curve.