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- Hamming_code abstract "In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code 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 3.In mathematical terms, Hamming codes are a class of binary linear codes. For each integer there is a code with block length and message length .Hence the rate of Hamming codes is , which is highest possible for codes with minimum distance (i.e. the minimal number of bit changes needed to go from any code word to any other code word is 3) and block length .The parity-check matrix of a Hamming code is constructed by listing all columns of length that are non-zero, which means that the dual code of the Hamming code is the punctured Hadamard code. The parity-check matrix has the property that any two columns are pairwise linearly independent.Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory (ECC memory), where bit errors are extremely rare and Hamming codes are widely used. In this context, an extended Hamming code having one extra parity bit is often used. Extended Hamming codes achieve a Hamming distance of , which allows the decoder to distinguish between when at most one bit error occurred and when two bit errors occurred. In this sense, extended Hamming codes are single-error correcting and double-error detecting, abbreviated as SECDED.".
- Hamming_code thumbnail Hamming(7,4).svg?width=300.
- Hamming_code wikiPageExternalLink hamming.pl.
- Hamming_code wikiPageExternalLink book.html.
- Hamming_code wikiPageExternalLink book.html.
- Hamming_code wikiPageExternalLink Mathematical-Challenge-April-2013.pdf.
- Hamming_code wikiPageID "41226".
- Hamming_code wikiPageRevisionID "604986664".
- Hamming_code alphabetSize "2".
- Hamming_code blockLength "where".
- Hamming_code hasPhotoCollection Hamming_code.
- Hamming_code imageCaption "The Hamming-code".
- Hamming_code name "Binary Hamming Codes".
- Hamming_code namesake Richard_Hamming.
- Hamming_code notation "-code".
- Hamming_code properties Hamming_bound.
- Hamming_code type Block_code.
- Hamming_code subject Category:American_inventions.
- Hamming_code subject Category:Coding_theory.
- Hamming_code subject Category:Computer_arithmetic.
- Hamming_code subject Category:Error_detection_and_correction.
- Hamming_code type Ability105616246.
- Hamming_code type Abstraction100002137.
- Hamming_code type AmericanInventions.
- Hamming_code type Code106667317.
- Hamming_code type Cognition100023271.
- Hamming_code type Communication100033020.
- Hamming_code type Creativity105624700.
- Hamming_code type Invention105633385.
- Hamming_code type PsychologicalFeature100023100.
- Hamming_code type WrittenCommunication106349220.
- Hamming_code comment "In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code 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_code label "Code de Hamming".
- Hamming_code label "Codice di Hamming".
- Hamming_code label "Código Hamming".
- Hamming_code label "Código de Hamming".
- Hamming_code label "Hamming code".
- Hamming_code label "Hamming-Code".
- Hamming_code label "Hamming-code".
- Hamming_code label "Kod Hamminga".
- Hamming_code label "Код Хэмминга".
- Hamming_code label "ハミング符号".
- Hamming_code label "汉明码".
- Hamming_code sameAs Hammingův_kód.
- Hamming_code sameAs Hamming-Code.
- Hamming_code sameAs Código_Hamming.
- Hamming_code sameAs Hamming_kode.
- Hamming_code sameAs Code_de_Hamming.
- Hamming_code sameAs Codice_di_Hamming.
- Hamming_code sameAs ハミング符号.
- Hamming_code sameAs 해밍_부호.
- Hamming_code sameAs Hamming-code.
- Hamming_code sameAs Kod_Hamminga.
- Hamming_code sameAs Código_de_Hamming.
- Hamming_code sameAs m.0b9jj.
- Hamming_code sameAs Q853922.
- Hamming_code sameAs Q853922.
- Hamming_code sameAs Hamming_code.
- Hamming_code wasDerivedFrom Hamming_code?oldid=604986664.
- Hamming_code depiction Hamming(7,4).svg.
- Hamming_code isPrimaryTopicOf Hamming_code.