(a) x n - 1 = (x - l)q(x) in Z2[X], What is q(x)?

(b) Let 9 be the generator of the cyclic binary code C of length n. Show that if x - 1Ig(x) then all codewords have even weight.

(c) Show that q(x) (in (a)) is not a multiple of x-I if n is odd.

(d) Let n (in (b)) be odd, and suppose C has a word of odd weight. Show that 111 ... 1 E C and that the set of all even weight words of C is a cyclic code having (x - l)g(x) as its generator.