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In this work we present some results that allow to improve the decodingradius in solving polynomial linear systems with errors in the scenario whereerrors are additive and randomly distributed over a finite field. The decodingradius depends on some bounds on the solution that we want to recover, so theiroverestimation 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 theestimate decoding radius and the effective error correction capability.

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