6 problems

Let $q$ be a prime power, let $\mathcal H_q^{(3)}\subset\mathbb P^4$ be a Hermitian threefold, and let $S\subset\mathbb P^4$ be a hypersurface of degree $d\le q$, all defined over…

Edoukou–Ling–Xing conjecture. The maximum is

Let $q=t^2$, and let $\mathcal{X}\subset\mathbb{P}^{N}(\mathbb{F}_q)$ be the non-degenerate Hermitian variety defined by … Let $C_2(\mathcal{X})$ be the code obtained by evaluating…

Let $q=t^2$, and let $\mathcal{X}\subset\mathbb{P}^{4}(\mathbb{F}_q)$ be the non-degenerate Hermitian variety defined by … For a degree-$h$ form $f$, write $Z(f)$ for its zero hype…

Let $q$ be a prime power, let $\mathcal H_q^{(2)}\subset\mathbb P^3$ be a nondegenerate Hermitian surface defined over $\mathbb F_{q^2}$, and let $S\subset\mathbb P^3$ be a degree-…

Let $q=t^2$, and let $\mathcal{X}$ be the non-degenerate Hermitian variety in $\mathbb{P}^{n}(\mathbb{F}_q)$ defined by … For the functional code $C_h(\mathcal{X})$, let $w_i$ deno…