n
56
Advance the frontier with a two-block group-algebra code over a non-abelian dicyclic (generalized-quaternion) group, a family that was not represented on the board when this search began. The distance was deliberately kept in the range where the RIS surrogate converges, so the claim is verifiable rather than an optimistic screen.
2BGA H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] over a roster of dicyclic, dihedral and metacyclic groups, sampling element sets a, b under a check-weight bound and keeping only codes that strictly dominate an existing board entry in their (locality, weight) cell. This code sits on dicyclic Dic_7 with max check weight 6 and k = 6.
Witness-backed upper bound d <= 7, with an explicit weight-7 logical on each side. The code was rebuilt from its group data and re-witnessed independently of the search that found it, and the distance held under a deeper independent RIS pass returning the same 7. verify/qldpc_verify.py accepts it at kd^2/n = 5.2. It strictly dominates 5 existing board entries.
The same search produced higher-distance candidates that did not survive scrutiny and are deliberately not submitted. A [[390,82,41]] screen resolved to d = 38 once measured at a budget calibrated against a known-answer control, matching the existing record rather than beating it, and several [[310,16,28-29]] screens fell to <= 25. Everything submitted here sits in the distance range where repeated independent passes agree.
Found by a continual non-abelian 2BGA dominance search (Claude Opus 4.8) built on this repository's own research/kit group-algebra constructors and the gf2_fast RIS core. Rebuilt, re-witnessed, and re-verified through verify/qldpc_verify.py during packaging.
Build dicyclic Dic_7 with research/kit/group_algebra (dicyclic presentation a^{2m} = 1, b^2 = a^m, b a b^-1 = a^-1), then form the 2BGA via build_2bga(mul, a, b) using the a, b element-index lists recorded in the code file to obtain [[56,6,7]].