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Hamming code 汉明码

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The same [7,4] example from above with an extra parity bit. This diagram is not meant to correspond to the matrix H for this example.
Anordnung der Paritäts-Kontrollstellen p1…pk und der Datenbits d1…dN-k in einem Codewort mit den Stellen c1…cN für die im Folgenden dargestellte Bitanordnung.
(15,11)-Hamming-Code-Encoder.

In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code, and were invented by Richard Hamming in 1950. Hamming codes can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.

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