7 problems

Neumaier's conjecture. The only completely regular code containing more than two codewords with $d\geq 8$ is the extended binary Golay code.

Let $C$ be a $q$-ary completely regular code with covering radius $\rho$ and covering error-correcting capability $e$. Assume that $|C|>2$. External-distance conjecture. Then … Thi…

Classification conjecture. These codes comprise only the classic examples of Cameron–Liebler line classes: a point, a hyperplane, and a nonincident point–hyperplane pair.

Let $C^{(i)}$ be the nested binary codes defined in the paper, with parameter $u$ and $i ein{0,1,ldots,u}$. Complete transitivity conjecture. The code $C^{(i)}$ is completely t…

Neumann's packing-radius conjecture. The packing radius satisfies

Let $C$ be a completely regular code in a Hamming graph, and let its covering radius be the maximum distance from a vertex of the Hamming graph to $C$. Leonard conjecture. All comp…

Neumaier's conjecture. The error-correcting capability satisfies