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：本文提出一种快速算法，用于实现代数几何码的Guruswami-Sudan列表译码实例。我们证明：任意此类码可在底层有限域上以$\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\omega)$次运算完成译码，其中$n$为码长，$g$为构造该码所用的函数域的亏格，$s$为重数参数，$\ell$为设计列表大小，$\mu$为某选定位置的Weierstrass半群中的最小正元素。