Symmetric matrices and codes correcting rank errors beyond the image bound Original Research Article

Rank codes can be described either as matrix codes over the base field image or as vector codes over the extension field image. For any matrix code, there exists a corresponding vector codes, and vice versa. We investigate matrix codes containing a linear subcode of symmetric matrices. The corresponding vector codes contain a linear subspace of so-called symmetric vectors. It is shown that such vector codes are generated by self-orthogonal bases of the field image If code distance is equal to image, than such codes can correct not only all the errors of rank up to image but also many symmetric errors of rank beyond this bound.