A linear-in-$q$ range of dimensions for the MDS conjecture over ${\mathbb{F}}_q$ in odd characteristic

Xiang Fan

Let $q$ be a power of an odd prime $p$. We prove the MDS conjecture over ${\mathbb{F}}_q$ in every dimension $k$ satisfying \[ 2\leqslant k\leqslant B(p,q) \quad\text{or}\quad q+2-B(p…