4(a) [20 marks] Construct the finite field of order 16 using a 5-term irreducible quartic poly-nomial

4(a) [20 marks] Construct the finite field of order 16 using a 5-term irreducible quartic poly-nomial. List the elements of the field in a four-column table, with the fourth column having the vector form of the elements, the third column having the polynomial form in terms of a primitive element a, the second column having the exponential form in terms of a where possible and the first column having the discrete logarithms of the terms in the second column (when they exist). Explain how you have produced the polynomial form from each exponential form where the exponent is greater than 4.