Hamming code

Hamming code Hamming codes are the primary class of single-error-correcting codes. Number of nonzero syndromes of an block code is: . Number of single-error patterns is n . Then, to correct every single error inequality (6.4.1) has to be fulfilled:
In general, number of all errors up to errors is: .
Then, to correct all errors up to errors, inequality (6.4.2) has to be fulfilled:
. For the Hamming code: and equality (6.4.3) is fulfilled:
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