= Extended Hamming code
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Adding an overall <parity bit> to the <Hamming code of length seven> gives an eight-bit <linear code> with <minimum Hamming distance> four: every resulting weight is <even>, every original nonzero weight is at least three, and a weight-three word extends to weight four. Thus it detects up to three errors when testing <codeword> membership and corrects one error. Joint single-error correction and double-error detection uses the overall parity together with the seven-bit <syndrome>.
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