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In coding theory, rank codes (also called Gabidulin codes) are non-binary linear error-correcting codes over not Hamming but rank metric. They described a systematic way of building codes that could detect and correct multiple random rank errors. By adding redundancy with coding k-symbol word to a n-symbol word, a rank code can correct any errors of rank up to t = ⌊ (d − 1) / 2 ⌋, where d is a code distance. As an erasure code, it can correct up to d − 1 known erasures. A rank code is an algebraic linear code over the finite field similar to Reed–Solomon code.

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rdfs:label
  • Rank error-correcting code (en)
  • Ранговый код (ru)
rdfs:comment
  • Ранговый код — алгебраический линейный код над полем , в общем случае — метод кодирования информации с целью защиты от помех. В настоящее время предложено использование данного кода для использования в случайном сетевом кодировании. В отличие от других алгебраических кодов, использующих метрику Хемминга, используется новая ранговая метрика (ранговое расстояние), которое задаётся как ранг разности векторов над полем . Ранговый код позволяет исправлять ошибки в передаваемой информационной матрице, если ранг ошибки не выше заданного. (ru)
  • In coding theory, rank codes (also called Gabidulin codes) are non-binary linear error-correcting codes over not Hamming but rank metric. They described a systematic way of building codes that could detect and correct multiple random rank errors. By adding redundancy with coding k-symbol word to a n-symbol word, a rank code can correct any errors of rank up to t = ⌊ (d − 1) / 2 ⌋, where d is a code distance. As an erasure code, it can correct up to d − 1 known erasures. A rank code is an algebraic linear code over the finite field similar to Reed–Solomon code. (en)
name
  • Rank codes (en)
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distance
  • n − k + 1 (en)
has abstract
  • In coding theory, rank codes (also called Gabidulin codes) are non-binary linear error-correcting codes over not Hamming but rank metric. They described a systematic way of building codes that could detect and correct multiple random rank errors. By adding redundancy with coding k-symbol word to a n-symbol word, a rank code can correct any errors of rank up to t = ⌊ (d − 1) / 2 ⌋, where d is a code distance. As an erasure code, it can correct up to d − 1 known erasures. A rank code is an algebraic linear code over the finite field similar to Reed–Solomon code. The rank of the vector over is the maximum number of linearly independent components over . The rank distance between two vectors over is the rank of the difference of these vectors. The rank code corrects all errors with rank of the error vector not greater than t. (en)
  • Ранговый код — алгебраический линейный код над полем , в общем случае — метод кодирования информации с целью защиты от помех. В настоящее время предложено использование данного кода для использования в случайном сетевом кодировании. В отличие от других алгебраических кодов, использующих метрику Хемминга, используется новая ранговая метрика (ранговое расстояние), которое задаётся как ранг разности векторов над полем . Ранговый код позволяет исправлять ошибки в передаваемой информационной матрице, если ранг ошибки не выше заданного. (ru)
alphabet size
  • Q = qN (en)
block length
  • n (en)
decoding
hierarchy
message length
  • k (en)
notation
  • [n, k, d]-code (en)
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