In this paper we consider algebraic geometry (AG) codes: a class of codes constructed from algebraic codes (equivalently, using function fields) by Goppa. These codes can be list-decoded using the famous Guruswami-Sudan (GS) list-decoder, but the genus $g$ of the used function field gives rise to negative term in the decoding radius, which we call the genus penalty. In this article, we present a GS-like list-decoding algorithm for arbitrary AG codes, which we call the \emph{inseparable GS list-decoder}. Apart from the multiplicity parameter $s$ and designed list size $\ell$, common for the GS list-decoder, we introduce an inseparability exponent $e$. Choosing this exponent to be positive gives rise to a list-decoder for which the genus penalty is reduced with a factor $1/p^e$ compared to the usual GS list-decoder. Here $p$ is the characteristic. Our list-decoder can be executed in $\tilde{\mathcal{O}}(s\ell^{\omega}\mu^{\omega-1}p^e(n+g))$ field operations, where $n$ is the code length.

翻译：本文研究代数几何（AG）码：一类由Goppa利用代数码（等价地，使用函数域）构造的码。这类码可通过著名的Guruswami-Sudan（GS）列表译码器进行列表译码，但所使用的函数域的属$g$会在译码半径中产生负项，我们称之为属种惩罚。本文针对任意AG码提出一种类GS列表译码算法，称之为\emph{不可分GS列表译码器}。除GS列表译码器常见的重数参数$s$和设计列表大小$\ell$外，我们引入不可分指数$e$。选择该指数为正时，所得列表译码器的属种惩罚相比于传统GS列表译码器将减少$1/p^e$倍，其中$p$为特征。我们的列表译码器可在$\tilde{\mathcal{O}}(s\ell^{\omega}\mu^{\omega-1}p^e(n+g))$次域运算内执行，其中$n$为码长。