4 problems

Let $q$ be the size of the finite field and let an NMDS code be a $q$-ary code of length $n$. Length bound conjecture. It has been conjectured that … This conjectured upper bound w…

Let $\mathscr{G}_{n,m}$ be the code in the family indexed by $n$ and $m$, and let $\mathscr{G}_{n,m}^{\bot}$ be its dual. Denote their relevant covering multiplicities by…

NMDS maximal-length conjecture. For all prime powers $q$, the maximal length for $q$-ary nontrivial NMDS codes is at most $2q+2$. This is the proposed analogue of the MDS main conj…

Let $q=2^m$ with $m\geq k_1\geq 3$, where $k_1$ is some proper positive integer. Let $\alpha_1,\alpha_2,\ldots,\alpha_{q-1}$ be all elements of $\mathbb{F}_q^*$. For $2<k<q-1$, def…