Let $C$ be a  $[n, k]$ linear code over $\mathbb{F}_q$.I want to calculate the covering radius of the Hamming codes.I have thought the following:Since the Hamming distance is $3$, the coverig radius will always be $3$.Am I right?
Covering radius of code
coding theory
The Hamming codes are perfect codes. This means that balls of radius $(d-1)/2$ (where $d$ is the minimal distance) centered around the codewords partition the space. In particular, the covering radius is $(d-1)/2$.