For each of the codes C $=($S$)$ with S defined below, find the generator

polynomial g $($x$)$ and then represent each word in the code as a multiple of g $($x$).$

$($a$)$ S $=\{010,011,111\}($b$)$ S $=\{1010,0101,1111\}$

$($c$)$ S $=\{0101,1010,1100\}($d$)$ S $=\{1000,0100,0010,0001\}$

$($e$)$ S$=\{11000,01111,11110,01010$