Definition of Minimum Code Distance

Let $C$ be a code and $d$ its Hamming distance function. The (minimum) distance of $C$, denoted by $d_{\text{min}}(C)$, is the smallest Hamming distance possible achieved by two (distinct) codewords of $C$.

Mathematically,

$$d_{\text{min}}(C):=\text{min}\{d(c_1,c_2):c_1,c_2\in C,c_1\ne c_2\}$$