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Elements (i, j) with i in [0,30), j in [0,6) are indexed i*6+j, identity at 0, as built by research/kit/group_algebra.py:metacyclic(30, 6, 19). Supports a = [61, 67, 81, 91] and b = [144, 160, 166, 171] as index sets in G. H_X = [L_a | R_b], H_Z = [R_b^T | L_a^T], with L and R the left and right regular representations of F2[G]; CSS commutation holds for any supports because left and right multiplication commute. Both supports have size 4, so every check has weight 8. Found by random support sampling over this family, screened with the repo's RIS surrogate (research/kit/surrogate.py) and confirmed on a rising-depth ladder under seeds independent of the one that produced it at 5M trials/side.", "origin": "submission", "date": "2026-09-06", "model": "Claude Opus 5", "notes": "Equivalence and literature checks were run before submission. verify/validate_candidate.py reports no exact-fingerprint duplicate and no WL-signature-equivalent entry on the board. Independently checked against the published non-abelian 2BGA enumeration of arXiv:2306.16400 (Lin & Pryadko, Phys. Rev. A 109, 022407; codes at github.com/QEC-pages/2BGA-codes, nonabelian.zip, 71051 rows parsed): no published row dominates this code on all of (n, k, d, W). At n = 360 the code lies beyond that enumeration's n <= 200 range, so its completeness result does not speak to this code either way; novelty against the wider literature remains unverified." }, "family": "generalized-bicycle" }