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- Justesen_code abstract "In coding theory, Justesen codes form a class of error-correcting codes that have a constant rate, constant relative distance, and a constant alphabet size.Before the Justesen code was discovered, no code was known that had all of these three parameters as a constant.Subsequently, other codes with this property have been discovered, for example expander codes.These codes have important applications in computer science such as in the construction of small-bias sample spaces.Justesen codes are derived as the code concatenation of a Reed–Solomon code and the Wozencraft ensemble.The Reed–Solomon codes used achieve constant rate and constant relative distance at the expense of an alphabet size that is linear in the message length.The Wozencraft ensemble is a family of codes that achieve constant rate and constant alphabet size, but the relative distance is only constant for most of the codes in the family.The concatenation of the two codes first encodes the message using the Reed–Solomon code, and then encodes each symbol of the codeword further using a code from the Wozencraft ensemble – using a different code of the ensemble at each position of the codeword.This is different from usual code concatenation where the inner codes are the same for each position.The Justesen code can be can constructed very efficiently using only logarithmic space.".
- Justesen_code wikiPageExternalLink FT02.
- Justesen_code wikiPageExternalLink coding-theory.
- Justesen_code wikiPageID "18557138".
- Justesen_code wikiPageRevisionID "563440023".
- Justesen_code alphabetSize "2".
- Justesen_code distance "where for small .".
- Justesen_code hasPhotoCollection Justesen_code.
- Justesen_code name "Binary Justesen Codes".
- Justesen_code namesake "Jørn Justesen".
- Justesen_code notation "-code".
- Justesen_code properties "constant rate, constant relative distance, constant alphabet size".
- Justesen_code type Block_code.
- Justesen_code subject Category:Coding_theory.
- Justesen_code subject Category:Error_detection_and_correction.
- Justesen_code subject Category:Finite_fields.
- Justesen_code type Field108569998.
- Justesen_code type FiniteFields.
- Justesen_code type GeographicalArea108574314.
- Justesen_code type Location100027167.
- Justesen_code type Object100002684.
- Justesen_code type PhysicalEntity100001930.
- Justesen_code type Region108630985.
- Justesen_code type Tract108673395.
- Justesen_code type YagoGeoEntity.
- Justesen_code type YagoLegalActorGeo.
- Justesen_code type YagoPermanentlyLocatedEntity.
- Justesen_code comment "In coding theory, Justesen codes form a class of error-correcting codes that have a constant rate, constant relative distance, and a constant alphabet size.Before the Justesen code was discovered, no code was known that had all of these three parameters as a constant.Subsequently, other codes with this property have been discovered, for example expander codes.These codes have important applications in computer science such as in the construction of small-bias sample spaces.Justesen codes are derived as the code concatenation of a Reed–Solomon code and the Wozencraft ensemble.The Reed–Solomon codes used achieve constant rate and constant relative distance at the expense of an alphabet size that is linear in the message length.The Wozencraft ensemble is a family of codes that achieve constant rate and constant alphabet size, but the relative distance is only constant for most of the codes in the family.The concatenation of the two codes first encodes the message using the Reed–Solomon code, and then encodes each symbol of the codeword further using a code from the Wozencraft ensemble – using a different code of the ensemble at each position of the codeword.This is different from usual code concatenation where the inner codes are the same for each position.The Justesen code can be can constructed very efficiently using only logarithmic space.".
- Justesen_code label "Justesen code".
- Justesen_code sameAs m.04f_c_7.
- Justesen_code sameAs Q13640215.
- Justesen_code sameAs Q13640215.
- Justesen_code sameAs Justesen_code.
- Justesen_code wasDerivedFrom Justesen_code?oldid=563440023.
- Justesen_code isPrimaryTopicOf Justesen_code.