Decoding of Space-Symmetric Rank Errors

This paper investigates the decoding of certain Gabidulin codes over a channel with space-symmetric errors. Space-symmetric errors are additive error matrices that have the property that their column and row spaces are equal. We show that for channels restricted to space-symmetric errors, with high probability errors of rank up to $2 (n-k)/3$ can be decoded with a Gabidulin code of length $n$ and dimension $k$ , using a weak-self orthogonal basis as code locators.