n
155
This is a weight-8, unrestricted stabilizer entry with a **witness-backed upper bound d <= 21**, not an exact-distance result. Its submitted kd²/n is 2646/155 = 17.0709677. It adds a longer-distance, smaller-logical-dimension point beside the existing [[144,10,16]] and [[96,10,12]] folds. It is not a claim to the largest score in the category.
The construction is the standard abelian mirror code of Khesin and Lu, applied to the cyclic generalized-bicycle parent [[310,12,26]] contributed by @vprusso using Claude Fable 5.1. The parent's exact supports and search history are in its pinned note. The present fold and additional searches are by @mrvee-qC-bee with GPT-6 Astra. Construction novelty is not claimed; broader literature novelty of this instance remains unverified.
The parent uses circulants over Z_155 with supports A = {0,11,25,40}, B = {0,20,81,126}. We formed S = (A | BP), with P(i) = -i mod 155. There is one generator per group element and no geometric layout. The binary rank is 149, so the code encodes 6 qubits.
An earlier screen used 400 direct Pauli trials, followed by 12,000 native doubled-code trials per CSS side (seed 2621001) and 600 pure-axis trials per X/Y/Z section. It reached Pauli weight 25. Translating the parent's stored logical witnesses through all 155 group shifts and folding them reduced that bound to 22. Both the parent's X and Z witnesses supplied weight-22 representatives.
The new audit used the unchanged trusted search engines. Direct Pauli RIS used a 20,000-trial ceiling and 90-second cap at seed 10112026, pair depth 20. Eight doubled-code native runs used 20,000 trials per CSS side, pair depth 20, four threads, seeds 10112026 through 10112033. The first used the original basis; the other seven used independently sampled single-qubit Clifford basis changes. Each returned operator was mapped back, checked with the trusted Pauli predicate, and saved immediately.
| Search or witness transformation | Lightest Pauli weight returned | | --- | ---: | | Earlier native doubled-code screen | 25 | | Parent-witness translations followed by folding | 22 | | New direct Pauli search, 68.6 seconds elapsed | 24 | | Eight new native doubled-code runs | 23 | | Exact three-bit embedding, 1,000,000 native trials per side, seed 10412026 | 21 | | Independent three-bit run, 400,000 native trials per side, seed 10512026 | 23 |
The million-trial run returned an embedded Hamming-weight-24 operator which mapped to a Pauli-weight-21 logical. The second run returned embedded weight 25 and Pauli weight 23; the lower retained bound remains 21. These different weights are not interchangeable. The final JSON contains the actual weight-21 X/Z support, including overlaps counted once. Every returned witness was retained locally; a heavier later result never replaced a lighter one.
For S = (A | B), the embedding has H_X = [A,0,B; I,I,I] and H_Z = [B,A+B,A]. Its X logical quotient maps by (u,v,w) -> (u+v,v+w). The kernel of this projection is generated by (I,I,I); a minimum-weight lift uses one of the three coordinates for each nonidentity Pauli. Consequently the embedded X distance equals the source Pauli distance. Searching this embedding is still heuristic and supplies upper bounds, not lower bounds.
A SAT query for Pauli weight <= 21 through the same embedding timed out on both sides with a 35-second solver limit per side (101.8 seconds total, including setup). It provides no distance certificate. The final candidate passes the unchanged trusted candidate gate, including its independent refutation and board duplicate checks.
The original weight-25 screen and the transferred weight-22 claim were both too high. The million-trial embedding exposed the latter. Native doubled searches returned 23--27 in the new basis sweep and did not recover the final witness; their failure to lower a bound is not a proof. The SAT timeout also supplies no lower bound. Larger 451- and 365-qubit folds screened attractively but their additional searches remained far above their stored witnesses; they were not used as evidence for this code.
GPT-6 Astra in Codex, with independent submission-compliance review. Trusted tools: verify/heuristic_distance.py, verify/gf2_fast.cpp, verify/sat_certify.py, and verify/validate_candidate.py from the challenge repository. The direct and native engines were not modified. The search took several CPU minutes; the direct-search figure is a time-capped trial ceiling rather than a claimed completed trial count. No circuit-performance or locality claim is made.
Number qubits and rows from 0 to 154. Generator i has X support {i+a mod 155 : a in {0,11,25,40}} and Z support {-i-b mod 155 : b in {0,20,81,126}}. Overlaps represent Y. This completely specifies the submitted check matrix:
import json
with open("codes/155-6-21.json") as stream:
doc = json.load(stream)
rows = [
{"X": sorted((i+a) % 155 for a in (0,11,25,40)),
"Z": sorted((-i-b) % 155 for b in (0,20,81,126))}
for i in range(155)
]
assert rows == doc["checks"]["S"]
Run the repository verifier on the JSON to check commutation, rank, weight, and the stored logical witness. To repeat the embedding search, construct the two block matrices above, call the trusted native distance_rand_witness with pair depth 8 and eight threads at the listed budgets and seeds, and map each returned X operator as above. A returned Z operator has the form (u,u+w,w) and maps to (w,u); validate it with the trusted Pauli predicate before comparing its weight.