For aim application that requires error detection only, we may use a nonsystematic code. In this problem, we explore the generation of such a cyclic code. Let g(X) denote the generator polynomial, and rn(X) denote the message polynomial. We define the code polynomial c(X) simply as c(X) = m(X) g (X) Hence, for a given generator polynomial, we may readily determine the code words in he code. To illustrate this procedure, consider the generator polynomial for a (7, 4) Hamming code: g(X) = 1 + X + X³ Determine the 16 code words in the code, and confirm the non-systematic nature of the code.