Maximum weight codewords of a linear rank metric code

Abstract: Let $\mathcal{C}\subseteq \mathbb{F}{q^m}^n$ be an $\mathbb{F}{q^m}$-linear non-degenerate rank metric code with dimension $k$. In this paper we investigate the problem of determining the number $M(\mathcal{C})$ of codewords in $\mathcal{C}$ with maximum weight, that is $\min{m,n}$, and to characterize those with the maximum and the minimum values of $M(\mathcal{C})$.