A systematic $(6,3)$ block code has the following generator matrix:

G$=$

$[110100$

$011010$

$101001]$

Answer the following questions.

$1.$ What is the code rate of this block code?

$2.$ Determine all the $8$ codewords of this code. What is dmin for this code?

$3.$ Construct the standard array for the code. Pick error patterns with the smallest Hamming Weight

as the coset leaders.

$4.$ Determine the corresponding syndromes for the coset leaders.