We wish to transmit an $n-$bit message to a receiving agent. The bits in the message are independently

corrupted $($flipped$)$ during transmission with $lon$ 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 $1-.$ What is the maximum feasible value of $n?$ Calculate this value for

the case $lon=0\mathrm{.}001,=0\mathrm{.}01.$