$.$ You may have noticed that compared to the $4-$bit message, the Hamming code appends a LOT of bits to the end. In fact it almost doubles the length of the message, using

of the vector just for the error checking! However, the number of error$-$checking bits scales very nicely with the size of the message, so for just one extra bit, we can send a much larger message. And if we use a few more error$-$checking bits, we can send very long messages $($although this isn't a good idea, because longer messages have a higher chance of multiple bit flips occurring$).$