Exercise $3.$ Consider all the possibile strings of two data bits $(K=2).$ A CRC is attached at the end

of each string during transmission to create the corresponding codework. The CRC is computed using the

generator polynomial $g(D)=D^3+1.$

A$)$ Generate all $4$ possible codewords $[$pt$.10].$

B$)$ Assume that at the receiver the received sequence of bits is affected by an error pattern described by

$e(D)=D^4+D^2+1.$ Regardless of what codeword is affected by this error, will the error be detected at

the receiver and why? $[$pt$.10].$

C$)$ Compute the distance between every pair of codewords, and the minimum distance of the code $d_{\text{m}\text{i}\text{n}}[$pt$.10].$

D$)$ Bonus points: List all error patterns $($using polynomial notation$)$ that cannot be detected by the chosen

pt$.10].$