We wish to transmit an $n$-bit message to a receiving agent. The bits in
the message are independently corrupted (flipped) during transmission
with $\epsilon$ probability each. With an extra parity bit sent along
with the original information, a message can be corrected by the
receiver if at most one bit in the entire message (including the parity
bit) has been corrupted. Suppose we want to ensure that the correct
message is received with probability at least $1-\delta$. What is the
maximum feasible value of $n$? Calculate this value for the case
$\epsilon{{,=,}}0.002$, $\delta{{,=,}}0.01$.