We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank can be corrected. Moreover, the corresponding family of decodable codes includes Gabidulin codes of rate $<1/2$. Second, for rates $>1/2$, we propose a decoder for Gabidulin codes correcting symmetric errors of rank up to $n-k$. The two mentioned decoders are deterministic and worst case.

翻译：我们考虑在误差矩阵对称的条件下对秩度量码进行译码。我们证明了两个结果。首先，对于码率$<1/2$的情况，存在一大类秩度量码，使得任意对称误差模式（即使具有最大秩）也能够被纠正。此外，相应的可译码家族包括码率$<1/2$的Gabidulin码。其次，对于码率$>1/2$的情况，我们提出了一种针对Gabidulin码的译码器，能够纠正秩高达$n-k$的对称误差。上述两种译码器均为确定性的且具有最坏情况性能。