 Bounded-distance decoding

For a code of minimum Hamming distance $d$ and radius $t$ with $2t<d$, bounded-distance decoding returns the unique codeword within Hamming distance $t$ of the received word, or reports failure if none exists. The disjointness of radius-$t$ Hamming balls gives uniqueness. It guarantees recovery when at most $t$ errors occurred, but a word produced by more errors can be nearer to a different codeword and be miscorrected.