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 $M(\mathcal{C})$.