Response to the following problem:
Let C1 and C2 denote two cyclic codes with the same block length n, with generator polynomials g1(X) and g2(X), and with minimum distances d1 and d2, respectively. Define Cmax = C1 ∪ C2 and Cmin = C1 ∩ C2.
1. Is Cmax a cyclic code? Why? If yes, what is its generator polynomial and its minimum distance?
2. Is Cmin a cyclic code? Why? If yes, find its generator polynomial. What can you say about its minimum distance?