3 problems

For every linear code $\mathcal{C}\subseteq\mathbb{F}_q^n$ of dimension $k$ over every finite field $\mathbb{F}_q$, and every admissible order $t$ with $1\le t\le k$, the $t$-th ge…

Let a ship start at the origin and follow an arbitrary deterministic unit-speed path $\gamma:[0,\infty)\to\mathbb{R}^2$. For every straight line $L\subset\mathbb{R}^2$ with…

For every integer $h\ge 2$ and every integer $n\ge 2h-2$, does there exist a collection of $h$ permutations $\pi_1,\ldots,\pi_h$ of $\{1,\ldots,n\}$ such that all proper partial su…