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.

中文翻译：

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增强同步有理函数恢复：自适应纠错能力和应用的新边界

在这项工作中，我们提出了一些结果，这些结果允许在求解具有错误的多项式线性系统时提高解码半径，其中错误是可加的并且随机分布在有限域上。解码半径取决于我们想要恢复的解决方案的某些界限，因此他们的高估可能会显着降低我们的纠错能力。出于这个原因，我们引入了一种可以弥补这一差距的算法，引入了一些临时参数，以减少估计解码半径和有效纠错能力之间的差异。