On Codes Correcting Symmetric Rank Errors

New Communication Models and Decoding of Maximum Rank Distance Codes

“…, e n−1 . X = −γ t /γ t if γ t + γ ′ t X = 0 and this solution can be verified by δ 2 , δ 3 and a known coefficient e i in (17). Substituting ( 16) in (8) gives…”

Decoding of Space-Symmetric Rank Errors

“…In [14], [16], the following channel model was considered. Let the Gabidulin codeword c = uG k be corrupted by an error e of rank rk(e) = t, that means…”

“…and E = φ(e) is a symmetric matrix. Then, errors of rank up to t ≤ (n − 1)/2 can be corrected for certain parameters [14], [16].…”

“…In [14]- [16] it was shown that for Gabidulin codes that contain a linear subcode of symmetric matrices (i.e., the transpose of the matrix coincides with the matrix itself) can correct symmetric error matrices of rank up to (n − 1)/2. In this paper, we relax the condition of symmetric errors and consider the case of space-symmetric error matrices which have the property that their column and row spaces coincides.…”

“…In this paper, we relax the condition of symmetric errors and consider the case of space-symmetric error matrices which have the property that their column and row spaces coincides. We show that it is possible to use a Gabidulin code with the same property as in [14]- [16] to decode such space-symmetric errors of rank up to 2(n − k)/3 with high probability. We further derive an upper bound on the failure probability of decoding such spacesymmetric errors including some simulation results to further support the validation.…”