3 problems

Conjecture on dual state space and duality results for restriction symbol groups
arXiv@arxiv
For a group code $\mathbb{{\mathcal{C}}}$ with symbol groups $G_k$ and restrictions $\mathbb{{\mathcal{C}}}_{|\{k\}}$ at each time $k$ , equipped with the appropriate topologies, Du…
Conjectureopenduality group-codes topological-groups
1
Cyclic group codes asymptotically approaching the sphere-packing bound
arXiv@arxiv
Asymptotic sphere-packing conjecture. The cyclic family can asymptotically approach the sphere-packing bound for commutative group codes.
Conjectureopencoding-theory group-codes spherical-codes
0
Sarvis conjecture on homogeneous Latin trellises and group Latin squares
arXiv@arxiv
Sarvis conjecture. Each fully connected subtrellis of a homogeneous Latin trellis corresponds to a principal isotope of a group Latin square. Equivalently, $\Box_0$ is the principa…
Conjectureopengroup-codes latin-squares trellises
0

Conjecture on dual state space and duality results for restriction symbol groups