I have a string $S$ of length (say) 34, that I know the first (say) 24 bytes of, but not the last 10. I also have the 10-byte error correcting code $RS_{44,34}(S)$ in full. Do I have any hope of recovering $S$?
The amount of information of $S$ that I'm missing far exceeds the theoretical guarantee of Reed-Solomon (which I think in this case is 3 bytes), but at the same time, there's $2^{80}$ possible values for the unknown portion of $S$, and also $2^{80}$ possible outputs for the error correction. If we were to iterate over all possible values for the unknown portion of $S$, I would naively expect approximately 1 of them to match the error correction. But $2^{80}$ is too much to brute force.
Are there any techniques that could recover (or at least reduce the state space for) an input, given its Reed-Solomon EC? Is there any reason to think one way or the other that RS is cryptographically secure in this sense?
For background, the "real world" application here is that I have a QR code (version 2, L-level EC) where I don't have the main data bits, but I do have the EC bits. I know that the data is a URL on a particular domain, thus the prefix.