I am looking for a secret sharing scheme that is robust against noise, the shares are going to be noisy. We do not want to reconstruct the secret perfectly and a noisy reconstruction with a bound on noise is good enough.
Assume we are using $(n,k)$ Shamir's scheme to distribute a secret among $n$ parties so that we need at least $k$ of them to recover. If we add noise to the shares, using $k$ points, the reconstructed polynomial would be very noisy. However, having access to an infinite amount of points would result in a perfect reconstruction. Are there any works that quantify this reconstruction noise?
If you know of any other idea or another sharing scheme, that would also be great!