a$.$ In a CRC error$-$decting scheme, choose P$($x$)=$ X$4+$ x $+1$; encode this bits: $100100111011$

b$.$ Suppose the channel introduces and error pattern: $100010000000000(15$bits$).($i$.$e$.$: a flip from $1$ to $0$ or from $0$ to $1$ in position $1$ and $5).$ What's received? Can the error be detected?