The generator polynomial of C(n = 8, k = 4) cyclic code is given as
g(x) = x4 + 1
(a) Find the parity check polynomial of this code.
(b) Express the data vector d = [1 0 1 1] in polynomial form, and encode the data polynomial using non-systematic and systematic encoding methods. Obtain the systematic and non-systematic code-word and determine the locations of both data and parity bits in each code-word.