$7\mathrm{.}9$ Based on Example $3\mathrm{.}4\mathrm{.}13($ii$),$ determine the following:

$($a$)$ the number of binary cyclic codes of length $21$ ;

$($b$)$ all values $k$ for which there exists a binary $21,k-$cyclic code;

$($c$)$ the number of binary $21,12-$cyclic codes;

$($d$)$ the generator polynomial for each of the binary $[21,12]-$cyclic codes.