Constructing Algebraic Geometry Codes on the Normalization of a Singular Cab Curve
نویسنده
چکیده
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. key words: one-point algebraic geometry code, Cab curve, evaluation code, normalization, Gröbner basis
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