Let $C$ be a $[n,k]$ linear code over $\mathbb{F}_q$.
Suppose that $\rho$ is the covering radius .
I want to show that $\rho \leq n-k$.
Could you give me a hint how we could show this?
The covering radius is defined as follows:
$$\rho=\max_{x \in \mathbb{F}_q^n} d(x,C) \\ d(x,C)=\min_{c \in C} d(x,c)$$