On the MDS conjecture in even characteristic

Abstract

We prove that every nontrivial linear $[n,k]$ maximum distance separable (MDS) code over a finite field \F_q of characteristic two satisfies $n\le q+1$, except in dimensions $k=3$ and $k=q-1$, where $n\le q+2$. This resolves the linear MDS conjecture in even characteristic.