Hamming code: Difference between revisions

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{{short description|Family of linear error-correcting codes}}

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In [[computer science]] and [[telecommunicationtelecommunications]], '''Hamming codes''' are a family of [[linear code|linear error-correcting codes]]. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the simple [[parity bit|parity code]] cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are [[perfect code]]s, that is, they achieve the highest possible [[Block code#The rate R|rate]] for codes with their [[block code#The block length n|block length]] and [[Block code#The distance d|minimum distance]] of three.<ref>[https://www.cs.cmu.edu/~venkatg/teaching/codingtheory/notes/notes1.pdf See Lemma 12 of]</ref>

[[Richard Hamming|Richard W. Hamming]] invented Hamming codes in 1950 as a way of automatically correcting errors introduced by [[punched card]] readers. In his original paper, Hamming elaborated his general idea, but specifically focused on the [[Hamming(7,4)]] code which adds three parity bits to four bits of data.{{Sfnp|Hamming|1950|pp=153&ndash;154}}