$4.(20$ points$)$ Consider $($n$,$ k$)$ code with minimum distance dmin $=$ $>0.($a$)$ Show that code rate satisfies Rc $1$ $1$ n $.($b$)$ Show that code rate satisfies Rc $1$ log$2$ $12$ j$=0$ n j n $.($c$)$ Show that a $(7,3)$ code that can correct up to $2$ errors does not exist.