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 $\tilde{O}(s^2\ell^{ω-1}μ^{ω-1}(n+g) + \ell^ωμ^ω)$ 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 $μ$ is the smallest positive element in the Weierstrass semigroup of some chosen place.

翻译：本文提出了一种快速算法，用于实现代数几何码的Guruswami-Sudan列表译码器的一个实例。我们证明，任何此类码都可以在底层有限域上以 $\tilde{O}(s^2\ell^{ω-1}μ^{ω-1}(n+g) + \ell^ωμ^ω)$ 次运算完成译码，其中 $n$ 为码长，$g$ 为用于构造该码的函数域的亏格，$s$ 为 multiplicity 参数，$\ell$ 为设计列表大小，$μ$ 为某个选定位置的Weierstrass半群中的最小正元素。