{
 "schema_version": "0.4",
 "name": "Two-block graph-state code with a transposed matching",
 "code_type": "stabilizer",
 "n": 16,
 "k": 2,
 "family": "other",
 "checks": {
  "S": [
   {
    "X": [
     0,
     1
    ],
    "Z": [
     0,
     1,
     3,
     6,
     8,
     9
    ]
   },
   {
    "X": [
     1,
     2
    ],
    "Z": [
     1,
     2,
     4,
     7,
     9,
     10
    ]
   },
   {
    "X": [
     2,
     3
    ],
    "Z": [
     0,
     2,
     3,
     5,
     10,
     11
    ]
   },
   {
    "X": [
     3,
     4
    ],
    "Z": [
     1,
     3,
     4,
     6,
     11,
     12
    ]
   },
   {
    "X": [
     4,
     5
    ],
    "Z": [
     2,
     4,
     5,
     7,
     12,
     13
    ]
   },
   {
    "X": [
     5,
     6
    ],
    "Z": [
     0,
     3,
     5,
     6,
     13,
     15
    ]
   },
   {
    "X": [
     6,
     7
    ],
    "Z": [
     1,
     4,
     6,
     7,
     14,
     15
    ]
   },
   {
    "X": [
     8,
     9
    ],
    "Z": [
     0,
     1,
     8,
     9,
     11,
     14
    ]
   },
   {
    "X": [
     9,
     10
    ],
    "Z": [
     1,
     2,
     9,
     10,
     12,
     15
    ]
   },
   {
    "X": [
     10,
     11
    ],
    "Z": [
     2,
     3,
     8,
     10,
     11,
     13
    ]
   },
   {
    "X": [
     11,
     12
    ],
    "Z": [
     3,
     4,
     9,
     11,
     12,
     14
    ]
   },
   {
    "X": [
     12,
     13
    ],
    "Z": [
     4,
     5,
     10,
     12,
     13,
     15
    ]
   },
   {
    "X": [
     13,
     14
    ],
    "Z": [
     5,
     7,
     8,
     11,
     13,
     14
    ]
   },
   {
    "X": [
     14,
     15
    ],
    "Z": [
     6,
     7,
     9,
     12,
     14,
     15
    ]
   }
  ]
 },
 "distance": {
  "d": 5,
  "P": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     0
    ],
    "Z": [
     0,
     3,
     4,
     5,
     8
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@hirobumii"
  ],
  "model": "GPT-6 Astra",
  "date": "2026-10-17",
  "origin": "submission",
  "novelty": "unknown",
  "construction": "Additive CWS construction on two C_8 squared graphs, with cross matching pi=[0,1,2,3,4,5,7,6]. For graph-state generators K_i=X_i Z_(N(i)), take K_i K_(i+1) for i=0,...,6 in each block. The two block-even label subspaces give 14 independent weight-six checks.",
  "references": [
   "Cross, Smith, Smolin and Zeng, Codeword Stabilized Quantum Codes, arXiv:0708.1021v4; IEEE Transactions on Information Theory 55, 433-438 (2009). https://arxiv.org/abs/0708.1021v4",
   "Grassl, Bounds on additive quantum codes: [[16,2,6]] stored generator matrix. https://www.codetables.de/QECC.php?q=4&n=16&k=2"
  ],
  "notes": "Independently constructed instance within the established additive CWS framework; concrete code-space novelty is unverified. The known [[16,2,6]] means no unrestricted parameter record is claimed. This code is not obtained by relabeling a board entry. Fourteen independent weight-six checks, maximum qubit degree six, 84 incidences. The note includes a standalone reconstruction and exhaustive finite symplectic verification of distance five and a basis-independent non-LC-CSS argument. This is supplementary computational evidence, not an official exact certificate; distance.P.confidence remains upper_bound. No circuit, layout or LER claim. AI tools: GPT-6 Astra and GPT-6.1 Sol with OpenAI Codex. See notes/16-2-5.md."
 }
}