Using the factorization                 X 15 + 1 = (x+1)(x 2 +x+1)( x 4 +x+1)(x 4 +x 3 +x 2 +x+1)   (b) Find the generator polynomials of the cyclic codes C( n = 15, k = 11). (c) Find the generator...

                X¹⁵
+ 1 = (x+1)(x²+x+1)( x⁴+x+1)(x⁴+x³+x²+x+1)

(b) Find the generator polynomials of the cyclic codes C(n
= 15,
k
= 11).

(c) Find the generator polynomial, parity check polynomial, generator matrix, and parity check matrix of the cyclic code C(n
= 15,
k  = 7).