Definition of Nearest Neighbour Decoding

Given a code $C\subset A^n$ over an alphabet $A$ and a word $w\in A^n$, a (valid) codeword $c\in C$ is called a nearest neighbour codeword to $w$ if

$$d(c,w)=\text{min}\{d(w,x):x\in C\}$$

The nearest neighbour decoding strategy is the strategy of choosing a nearest neighbour codeword to a word received (possibly in error) in a transmission.

Note: there may be more than one nearest neighbour codeword!