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

TL;DR

This paper introduces an algorithm to improve the decoding radius for solving polynomial linear systems with random errors, enhancing error correction by better estimating bounds and reducing overestimation.

Contribution

The work presents a novel algorithm that adjusts bounds to improve the decoding radius in polynomial systems with errors, increasing error correction effectiveness.

Findings

Enhanced decoding radius for polynomial systems with errors

Algorithm reduces overestimation of bounds, improving correction capability

Better bounds lead to more reliable error correction in finite fields

Abstract

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.