7 problems

Let $\mathcal{C}$ be an $[n,k]$ MDS code over the finite field $\mathbb{F}_q$. Segre's MDS conjecture. Then … This conjecture concerns the maximum possible length of MDS codes over…

Let $q$ be a prime power, let $F\in\mathbb{F}_{q^2}[x_0,x_1,x_2,x_3]$ be homogeneous of degree $d$, and let $V_2\subset\mathbb{P}^3$ be a non-degenerate Hermitian surface defined o…

Let $q=t^2$ with $t$ a prime power, and let $X\subset\mathbb{P}^3$ be the hermitian surface … For a form $f$ of degree $h\leq t$, write $Z(f)$ for its zero locus and…

Let $\mathbb{X}$ be a finite set of reduced points in $\mathbb{P}^{s-1}$, and suppose that $I=I(\mathbb{X})$ is a complete intersection generated by $f_1,\ldots,f_c$, where $c=s-1$…

Let $I\subset S:=K[t_1,\ldots,t_s]$ be a complete intersection graded ideal of dimension $1$, generated by forms $f_1,\ldots,f_c$ with $c=s-1$, where $d_i=\deg(f_i)$ and…

Let $\mathbb{X}$ be a finite set of points in $\mathbb{P}^{s-1}$, and let $I(\mathbb{X})$ be its vanishing ideal. Suppose that $I(\mathbb{X})$ is a complete intersection generated…

Complete-intersection distance conjecture. Then