标题： 增强同时有理函数恢复：自适应错误纠正能力和新的应用界限 显示英文标题

标题： Enhancing simultaneous rational function recovery: adaptive error correction capability and new bounds for applications

摘要： 在本工作中，我们提出了一些结果，这些结果有助于在误差在有限域上随机分布的场景下，解决带有误差的多项式线性系统时提高解码半径。 解码半径取决于我们想要恢复的解的一些界限，因此它们的高估可能会显著降低我们的纠错能力。 因此，我们引入了一个算法，可以弥补这一差距，引入了一些专门设计的参数，以减少估计的解码半径与实际纠错能力之间的差异。 显示英文摘要

摘要： In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius depends on some bounds on the solution that we want to recover, so their overestimation could significantly decrease our error correction capability. For this reason, we introduce an algorithm that can bridge this gap, introducing some ad hoc parameters that reduce the discrepancy between the estimate decoding radius and the effective error correction capability.