2 problems

Let $k\leq n$, let $\mathbb{F}$ be an extension field of $\mathbb{F}_q$, and let $\mathcal{S}=(S_1,\ldots,S_k)$ be a zero pattern with $S_i\subseteq[n]$. A linear code attains…

Steiner triple code embedding-dimension conjecture. For every $d\ge 1$ there exists a Steiner triple code $\mathcal{C}$ with