Question $3.$

The Hamming distance function is very important in coding theory. It gives

a measure of the difference between two strings of $0\text{'}$s and $1\text{'}$s that have the

same length. Let $S_n$ be the set of all strings of $0\text{'}$s and $1\text{'}$s of length $n.$ The

Humming function $H$ is defined as follows:

$H$:$S_n{S}_{n}u\{0\}$

$(s,t)H(s,t)=$ The number of positions in which s and t have different values.

For $n=5,$ Find $H(11111,00000),H(11000,00000),H(00101,01110)$ and

$H(10001,01111).$