Q$.5(6$ Points$)$

At the receiver the syndrome for a Hamming coded data was$=[00100],$ in what bit there is an error, and what is the code rate.

Q$.6(6$ Points$)$

Draw and label the Encoder and the state diagram for the $(2,1,2)$ C$.$C that use the following connection polynomials then find the free distance: $g_0(x)=1+x+x^2{g}_1(x)=1$