7 problems

Reversibility and reversible complementarity conjecture. The code $Q$ is reversible, and also reversible complement, if and only if $l\lneq m$ and there exists a row $g(x)$ in $G$…

Uniqueness conjecture. There are no other $[54,27,10]$ self-dual cubic codes over ${\mathbb F}_2$.

Completeness conjecture. There exist no more binary cubic self-dual codes with length $54$, $60$, and $66$.

Generator matrix conjecture. A generator matrix in $\mathbb{F}_q[X]^{\ell\times\ell}$, in Pre-RGB/POT form, for the $[n=\ell m,k_Ak_B,d_Ad_B]_q$ $\ell$-quasi-cyclic product code…

Minimum-distance conjecture. The minimum distance of $\mathcal{C}_4$ is close to $68$.

Minimum-distance conjecture. The minimum distance is equal or close to the upper bound $48$.

Let $P$ be a quasi-cyclic code, and let $H'(P)$ denote the set of permutations by which two quasi-cyclic codes can be equivalent. Group conjecture for $H'(P)$. The set $H'(P)$ is a…