Let C be a binary cyclic code with generator polynomial g(x), and let C ' be the set of all codewords of even weight in C.

(a) Show that C ' is also a cyclic code.

(b) Show that if C contains a codeword of odd weight, then g(x) not belong to C '

(c) If C contains a codeword of odd weight, what is the generator polynomial of C ' ? Justify your answer.

note:

by definition, the codeword in cyclic code can do the code shifting