Capacity-achieving non-bipartite graph codes
Construct linear [N,δ]q graph codes over symmetric zero-diagonal matrices that achieve the optimal rate R = (1−δ)^2 − o(1) for adversarial vertex erasures, matching the known capacity in the non-bipartite setting.
References
Finally, it remains an interesting open problem to construct $[N,\delta]_q$-graph codes achieving the optimal rate $R=(1-\delta)2-o(1)$. We have resolved this problem for bipartite graph codes, but the question for the non-bipartite case remains open.
— Optimal Erasure Codes and Codes on Graphs
(Chen et al., 3 Apr 2025) in Concluding Remarks