Definition of Distance Theorem

Let $C$ be a code with minimal distance $d_{\text{min}}(C)$. Then the following statements hold:

1. If $t\in \mathbb{N}$ and $d_{\text{min}}(C)\ge t+1$, then $C$ detects $t$ errors.
2. If $k\in \mathbb{N}$ and $d_{\text{min}}(C)\ge 2k+1$, then $C$ corrects $k$ errors.

Note: this means that geometric information about a code can inform you on its error detection and correction ability!