Let $C$ be a linear $(n,k,d)$ -code over $\mb{F}_q$ .

The packing radius of $C$ is defined to be the value \begin{align*} \rho(C)=\frac{d-1}{2}. \end{align*} The covering radius of $C$ is \begin{align*} r(C)=\max_x\min_c \delta(x,c) \end{align*}with $x\in \mb{F}_q^n$ and $c\in C$ , and where $\delta$ denotes the Hamming distance on $\mb{F}_q^n$ .

The code $C$ is said to be perfect if $r(C)=\rho(C)$ .

The list of classes of linear perfect codes is very short, including only trivial codes, Hamming codes (i.e. $\rho=1$ ), and the binary and ternary Golay codes.