Q$)$ Consider the $(7,4)$ hamming code defined by the generator polynomial $g(x)=1+x+x^3.$ The code word $0111001$ is sent over a noisy, producing the received word $010100!$ that has single error.

a$.$ Determine the Generator matrix

b$.$ Also,determine thesyndrome polyonial $s(x)$ for the received, and show that it is identical to the error polynomial $e(x).$solve the question clearly with all steps