$4$ Error$-$Correcting Codes

$($a$)$ Recall from class the error$-$correcting code for erasure errors, which protects against up to $k$

lost packets by sending a total of $n+k$ packets $($where $n$ is the number of packets in the original

message$).$ Often the number of packets lost is not some fixed number $k,$ but rather a fraction

of the number of packets sent. Suppose we wish to protect against a fraction $$ of lost packets

$($where At least how many packets do we need to send $($as a function of $n$ and $)?$

$($b$)$ Repeat part $($a$)$ for the case of general errors.