Below question is a part of my assignment and I was completely clueless about where to start from. So, I am posting it here for the purpose of getting hints/resources to help me get started.
$ \ '' $To store $k$ blocks of data/information (say each block is of $b$ bits) in a fault-tolerant way, you may encode the $k$ blocks into $n$ blocks (using some error-correction code) such that if any $e$ of the $n$ blocks are corrupted, it is still possible to retrieve the original $k$ blocks of information. Specifically (for large enough $b$), coding theory suggests that this is possible if and only if $n \geq (k + 2e)$. However, show that using digital signatures, it is possible to achieve the above fault-tolerant storage even when $(k + e) \leq n \lt (k + 2e)$, assuming a PPTM-adversary(Probabilistic polynomial time) and a negligible probability of error is permitted.$ \ ''$