标题： AG码的更快列表解码 显示英文标题

标题： Faster List Decoding of AG Codes

摘要： 在本文中，我们提出了一种快速算法，用于执行代数几何码的Guruswami-Sudan列表解码器的一个实例。我们证明了任何此类码都可以在基础有限域中的$\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\omega)$次操作内进行解码，其中$n$是码长，$g$是用于构造码的函数域的亏格，$s$是多重性参数，$\ell$是设计的列表大小，$\mu$是某个选定点的Weierstrass半群中的最小正元素。 显示英文摘要

摘要： 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.