WebbThe first two constructions are based on subcodes of maximum rank distance codes, and the last one generates new codes from known Ferrers diagram rank metric codes. Each of these constructions produces optimal codes with different diagrams and parameters for which no optimal construction was known before. WebbThis bound is attained for all possible parameters and the codes which attain it are called maximum rank distance codes (or MRD codes in short). Let v be a vector of length n and …

An Assmus--Mattson Theorem for Rank Metric Codes

WebbWe present the theory of rank-metric codes with respect to the 3-tensors that generate them. We define the generator tensor and the parity check tensor of a matrix code, and … 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. highett fish and chips bluff road

A new family of linear maximum rank distance codes

WebbSuch a linear rank metric code always satisfies the Singleton bound [math]\displaystyle{ d \leq n - k + 1 }[/math]. Generating matrix. There are several known constructions of rank … WebbThe rank distance be- tween two matrices M1 and M2 is the rank of their difference Rk (M1 − M2 ). The rank distance of a matrix rank code M ⊂ FN q ×n is defined as the minimal pairwise distance: d (M) = d = min (Rk (Mi … Webb1 aug. 2024 · Gabidulin E.M.: Theory of codes with maximum rank distance (Translation). Probl. Inf. Transm. 1, 1---12 (1985). Gabidulin E.M., Paramonov A.V., Tretjakov O.V.: Ideals over a non-commutative ring and their application in cryptology. how high can wallabies jump