n
6
Small-blocklength cells on the CSS board are thinly covered, and the Error Correction Zoo (https://errorcorrectionzoo.org) publishes, for many entries, the exact stabilizer tableau and a three-parameter [[n,k,d]] claim. The question this note answers for one entry is narrow and useful: does a literature baseline with an explicit tableau already sit on the frontier, or is the board ahead of it? If a published code advances a cell, that cell is a thin one and worth searching; if every published code in a cell is dominated, searching that cell has to beat a stronger bar.
The source here is the zoo entry stab_6_4_2 (https://errorcorrectionzoo.org/c/stab_6_4_2), the self-complementary six-qubit code, unique for its parameters, whose stabilizer tableau is the two rows ZZZZZZ and XXXXXX.
A crawl of the zoo index, filtered to entries whose hierarchy path passes through a QLDPC concept, returned 681 quantum entries; 190 are primary qLDPC nodes, of which 35 state a three-parameter [[n,k,d]] claim. Each claim was bracketed against a snapshot of the live board before any matrix was built — exact match on (n,k,d), dominated in every track cell, records in some cells, or records in all of them. Only the claims that could advance a cell were built as matrices and submitted through the repository CLI. This code was one of three primary claims in the "records in all cells" bucket; two more were conditional on board type.
The verifier's witness search (20,000 random information-set trials, then the 2,000,000-trial accelerator pass) returned a witness of weight 2 on each side, so the claim is d <= 2, a witness-backed upper bound rather than a certified distance. Structural verification passed: CSS commutation, k = 4, max check weight 6, both witnesses valid.
The trusted gate verify/validate_candidate.py on the built document returned passed: true, with the label "advances the weight-6 x unrestricted board", no exact duplicate of any board entry, and no WL-equivalent entry. The claim is that it records in its own cell at submission time, not that it is a literature novelty — the gate reports literature novelty as unverified.
Of the 35 stated claims, 20 were already on the board as exact parameters and 9 were dominated in every cell they could land in. The zoo's [[30,8,3]] Bring code was not built: its generators have weight 5, which puts it in the weight-6 class where [[25,9,3]], [[30,10,3]] and [[30,8,4]] already dominate it, so no cell opens there.
Model Mimo-V2.6-Flash; repository CLI for the build and the witness search, and the repository's verify/ stack for the gate. Approximate compute: under a minute of CPU for the whole candidate.
Two checks on six qubits:
H_X = [1 1 1 1 1 1] (XXXXXX) H_Z = [1 1 1 1 1 1] (ZZZZZZ)
n = 6, k = 4, max check weight 6, distance witness 2. The CLI invocation that built and verified the entry in codes/6-4-2.json was ./qldpc submit with an .npz holding keys hx and hz, plus --authors @MathysRennela --model "Mimo-V2.6-Flash" --family other.
Cite the source: "([[6,4,2]] error-detecting code)", The Error Correction Zoo (V. V. Albert & P. Faist, eds.), https://errorcorrectionzoo.org/c/stab_6_4_2, arXiv:2606.11484.