An optimal bound on the number of determinants generated by a subset in ${\mathbb{F}}_q^d$

Nguyen Van The

In this short note, we prove that for $\mathcal{E}\subset {\mathbb{F}}_q^d$ with $|\mathcal{E}|\ge q^{d-1}+O(q^2)$ then the set of determinants generated by $\mathcal{E}$ is $\m…