Constructing algebraic geometry codes on the normalization of a singular C-ab curve
When we have a singular C-ab 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(infinity Q) having pairwise distinct pole orders at Q, where Q is the unique place of the C-ab curve at infinity. We present an algorithm finding such a basis from defining equations of the normalization of the original C-ab curve.
normalization c-ab curve one-point algebraic geometry code evaluation code grobner basis