  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.
