The covering radius of $C=\{0000,1111\}$

Question

Lets say I have the code $C=\{0000,1111\}$.

Why is the covering radius $\rho=2$?

How is the covering radius worked out?

Answer 1

You can consider the set of all posible tuples ($2^4$) divided in groups according to their weights (number of ones). With $\rho=1$ you cannot cover the tuples of weight 2 (the tuples that have two ones -eg $0011$- are at distance 2 from both codewords). With $\rho=2$ you cover all tuples.