Q$2.$ Consider $GF(8)$ generated using the "primitive polynomial" $x^3+x+1.$ Let $$ be a root of this polynomial. A $(7,5)$ Reed Solomon code over $GF(8)$ with generator polynomial

$g(x)=(x-)(x-{}^2)$

is used in a communication system. Suppose the received polynomial is

$r(x)=x^4+{}^4{x}^3+{}^3{x}^2+1$

Determine the transmitted codeword. Find the message polynomial $($that is$,$ divide the estimated codeword polynomial by the generator to obtain the message polynomial$).$