On additive MDS codes over small fields

Simeon Ball, Guillermo Gamboa, Michel Lavrauw

Let $C$ be a $(n,q^{2k},n-k+1{)}_{q^2}$ additive MDS code which is linear over ${\mathbb{F}}_q$. We prove that if $n⩾q+k$ and $k+1$ of the projections of $C$ are linear over…