Xiang Fan

A linear-in-$q$ range of dimensions for the MDS conjecture over $\mathbb F_q$ in odd characteristic

Let $q$ be a power of an odd prime $p$. We prove the MDS conjecture over $\mathbb F_q$ in every dimension $k$ satisfying$$ 2\leqslant k\leqslant B(p,q) \quad\text{or}\quad q+2-B(p,q)\leqslant k\leqslant q, \qquad B(p,q)=\left\lfloor\frac{(p-2)q+6p-10}{2p-3}\right\rfloor.$$For fix...

A linear-in-q range of dimensions for the MDS conjecture over F_q in odd characteristic

Let q be a power of an odd prime p. We prove the MDS conjecture over F_q in dimension k whenever 2 ≤ k ≤ B(p,q) or q + 2 − B(p,q) ≤ k ≤ q, where B(p,q) = ⌊((p − 2)q + 6p − 10)/(2p − 3)⌋. For fixed p, this gives a range of dimensions linear in q, in contrast with the square-root s...