标题： 评估码的列表解码 显示英文标题

标题： List decoding of evaluation codes

摘要： 多项式求值码在编码理论中占据重要地位。 在本工作中，我们研究了一类广义的多项式求值码，也称为环面码的列表解码问题，这些码是针对任何给定的凸多面体 P 定义的。例如 Reed-Solomon 码和 Reed-Muller 码等特殊情况已经得到了广泛研究。 我们提出了 Guruswami-Sudan 算法的一个推广，该算法考虑了 P 的几何结构和组合性质，并计算了解码半径的界限。 显示英文摘要

摘要： Polynomial evaluation codes hold a prominent place in coding theory. In this work, we study the problem of list decoding for a general class of polynomial evaluation codes, also known as Toric codes, that are defined for any given convex polytope P. Special cases, such as Reed-Solomon and Reed-Muller codes, have been studied extensively. We present a generalization of the Guruswami-Sudan algorithm that takes into account the geometry and the combinatorics of P and compute bounds for the decoding radius.