Say we have $N$ bits that we'd like to store in an $M$-bit error correcting code, where $M > N$. Given $\epsilon > 0$, as long as $N > N_0(\epsilon)$ we can recover the original bits as long as any $N(1+\epsilon)$ of the $M$ bits are correct.
Now say the bits are ordered in decreasing order of importance. Can we pick a single $M$-bit code so that if $K > K_0(\epsilon)$ out of the $M$ bits are uncorrupted, we can recover the first $K(1 - \epsilon)$ original bits correctly? Here the difference is that the code is independent of $K$.