8 problems

Maximum weight spectrum conjecture. The bound is sharp for all $q$ and $k$; that is, there exists a linear code of dimension $k$ over $\mathbb{F}_q$ with exactly…

Let $m$ and $t$ be integers, and let $C$ be obtained by adding an overall parity check to the primitive BCH code of length $2^m-1$ and designed distance $2t-1$. Thus $C$ has length…

Nu-function conjecture. For an arbitrary lattice $\Lambda$ of rank $n$,

Let $C$ be a binary linear code, and let $\sigma$ be a permutation in its permutation automorphism group $\operatorname{PAut}(C)$. Let $E_\sigma(C)$ denote the associated $\sigma$-…

Assmus–Mattson nonexistence conjecture. Then

Weight Enumerator Conjecture. The fixed space of $\mathcal{C}(\rho)$ is spanned by the full weight enumerators of codes of Type $\rho$.

Antipodal code coefficient conjecture. One has

Generalized Hamming polynomial reconstruction conjecture. The Tutte polynomial satisfies