In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\omega)$ operations in the underlying finite field, where $n$ is the code length, $g$ is the genus of the function field used to construct the code, $s$ is the multiplicity parameter, $\ell$ is the designed list size and $\mu$ is the smallest positive element in the Weierstrass semigroup of some chosen place.

翻译：在本文中，我们提出了一种快速算法，执行代数几何码的 Guruswami-Sudan 列表译码器的实例。我们证明任何此类码都可以在底层有限字段的 $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\omega)$ 次运算中进行解码，其中 $n$ 是码长，$g$ 是用于构建码的函数域的亏格，$s$ 是多重性参数，$\ell$ 是设计的列表大小，$\mu$ 是所选位置的 Weierstrass 半群中的最小正元素。