[[Code]]
# Quasi-perfect code

A $q$-ary [[code]] $\mathcal{C} \sube S_{q}^n$ of length $n$ in alphabet $S_{q}$ is said to be a **quasi-perfect $e$-correcting code** (cf. [[Perfect code]]), or briefly a **quasi-perfect code**, iff #m/def/code

- $e = \left\lfloor \frac{d-1}{2} \right\rfloor$ where $d$ is the [[Code#^minimumDistance]] of $\mathcal{C}$; and
- the [[Code#^coveringRadius]] of $\mathcal{C}$ is $e+1$.

## Properties

- The [[extended code]] of a [[Linear code|linear]] [[perfect code]] is quasi-perfect.

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