In this problem we work in the finite field 25, i.e. the numbers (mod 5) \small g(X)=X^2-6X+8=3+4X+X^2 , generator matrix follows from the above result as: \small \begin{pmatrix}3&4&1&0\\ 0&3&4&1\end{pmatrix} 5. What are the parity-check polynomial h(x) and the parity-check ma- trix H for the code C? 6. Show that c, where c = (1,1,1,1), is a codeword in C. 7. Consider et = (0,0,2,0). What is the syndrome of e? 8. A codeword c is transmitted, but there is an error and y=(3, 2, 2, 1) is received. Find c.