Consider the Hamming $(7,4)$ code Generator Matrix G$.$The Generator matrix for systematic Hamming $(7,4)$ code is given by

$G=\left[\begin{array}{ccccccc}1& 0& 0& 0& p_{11}& p_{12}& p_{13}\\ 0& 1& 0& 0& p_{21}& p_{22}& p_{23}\\ 0& 0& 1& 0& p_{31}& p_{32}& p_{35}\\ 0& 0& 0& 1& p_{41}& p_{42}& p_{43}\end{array}\right]$ Minimum Hamming distance produced by this

Generator Matrix can be computed by taking all possible pairs of $7-$bit codes

produced by this Matrix and determining the smallest Hamming distance between any

two pairs of $7-$bit codes. Using a method of your choice, determine the minimum

Hamming distance produced by this Generator matrix $$ please provide details on the

method you used to determine the minimum Hamming distance $$ for example, if you

used a piece of code attach that piece of code.