On the Dimension of the Space Generated by Characteristic Vectors of MRD Codes

ABSTRACT Given positive integers (), we call a rank‐metric code , with minimum distance for some , a maximum rank distance code (or MRD code for short) if . The space generated by MRD codes is defined to be the ‐vector space spanned by the characteristic vectors of all MRD codes. In this paper, we prove that its dimension equals , where the ‐th valency of the bilinear forms scheme, , is exactly the number of matrices of rank in .