$(10$ points$)$Find a generator and a parity$-$check matrix for the binary linear code generated by the $(10$ points$)$Find a generator and a parity$-$check matrix for the binary linear code generated by the

set $S=\{10101010,11001100,11110000,01100110,00111100\}$ and give the parameters $n,k,d$ for this

code.

set S $=\{10101010,11001100,11110000,01100110,00111100\}$ and give the parameters $[$n$,$ k$,$ d$]$ for this

code.