Coding theory | Error detection and correction

Rank error-correcting code

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. (Wikipedia).

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Related pages

Coding theory | Euclidean algorithm | Linear code | Finite field | Erasure code | Berlekamp–Massey algorithm | Reed–Solomon error correction | Random error