Consider a $(6,3)$ Hamming coding scheme with a data$-$word $\{$u$0,$ u$1,$ u$2\}$ and parity bits $\{$p$0,$ p$1,$ p$2\},$

which results in code$-$words as $\{$p$0,$ p$1,$ p$2,$ u$0,$ u$1,$ u$2\}.$ Parity bits are defined as follows;

p$0=$ u$0+$ u$2$

p$1=$ u$0+$ u$1$

p$2=$ u$1+$ u$2$

i$.$ Develop the Generator Matrix $($G$)$ for this coding scheme.