关于删余AG码的等距对偶性质的一个注记
A Note on the Inheritance of the Isometry-Dual Property under Puncturing AG Codes
摘要：
考虑AG码序列在一组求值点$P_1,\dots,P_n$处求值仅在定义点$Q$处具有极点的函数，其中码序列满足等距对偶条件（即，同时包含原始码和它们的对偶码）。我们证明了一个必要条件，在此条件下，在取出一些评价点（即打孔），所得到的AG码仍然可以满足等距对偶性质。这个条件与$Q$的Weierstrass半群的所谓最大稀疏理想有关。
英文摘要：
Consider a sequence of AG codes evaluating at a set of evaluation points $P_1,\dots,P_n$ the functions having only poles at a defining point $Q$, with the sequence of codes satisfying the isometry-dual condition (i.e. containing at the same time primal and their dual codes). We prove a necessary condition under which, after taking out a number of evaluation points (i.e. puncturing), the resulting AG codes can still satisfy the isometry-dual property. The condition has to do with the so-called maximum sparse ideals of the Weierstrass semigroup of $Q$.
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