{
 "schema_version": "0.4",
 "name": "[[21,1,7]]",
 "code_type": "stabilizer",
 "n": 21,
 "k": 1,
 "checks": {
  "S": [
   {
    "X": [
     10,
     11
    ],
    "Z": [
     1,
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     14,
     20
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   },
   {
    "X": [
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    "Z": [
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     15
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   },
   {
    "X": [
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    "Z": [
     1,
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     9,
     16
    ]
   },
   {
    "X": [
     13,
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    "Z": [
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     10,
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   },
   {
    "X": [
     14,
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    "Z": [
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     11,
     18
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   },
   {
    "X": [
     15,
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    "Z": [
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     19
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   },
   {
    "X": [
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    "Z": [
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   },
   {
    "X": [
     17,
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    "Z": [
     0,
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   },
   {
    "X": [
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    "Z": [
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   },
   {
    "X": [
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    "Z": [
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   },
   {
    "X": [
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    "Z": [
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   },
   {
    "X": [
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    "Z": [
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     18
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   },
   {
    "X": [
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    "Z": [
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     13,
     19
    ]
   },
   {
    "X": [
     2,
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    ],
    "Z": [
     6,
     12,
     14,
     20
    ]
   },
   {
    "X": [
     3,
     4
    ],
    "Z": [
     0,
     7,
     13,
     15
    ]
   },
   {
    "X": [
     4,
     5
    ],
    "Z": [
     1,
     8,
     14,
     16
    ]
   },
   {
    "X": [
     5,
     6
    ],
    "Z": [
     2,
     9,
     15,
     17
    ]
   },
   {
    "X": [
     6,
     7
    ],
    "Z": [
     3,
     10,
     16,
     18
    ]
   },
   {
    "X": [
     7,
     8
    ],
    "Z": [
     4,
     11,
     17,
     19
    ]
   },
   {
    "X": [
     8,
     9
    ],
    "Z": [
     5,
     12,
     18,
     20
    ]
   },
   {
    "X": [
     9,
     10
    ],
    "Z": [
     0,
     6,
     13,
     19
    ]
   }
  ]
 },
 "distance": {
  "d": 7,
  "P": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     8,
     9,
     13,
     14,
     15,
     19,
     20
    ],
    "Z": [
     8,
     13,
     14,
     15,
     20
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "One-block cyclic stabilizer code: generator X^a Z^b and its 21 cyclic shifts, a(x) = x^10 + x^11, b(x) = x^1 + x^7 + x^14 + x^20 in F_2[x]/(x^21 - 1); a = g p, b = g q with p, q palindromic so that a b* + b a* = 0; k = deg gcd(a, b, x^21 - 1)",
  "origin": "submission",
  "date": "2026-10-01",
  "model": "Claude Fable 5.1",
  "notes": "Found by a sweep of one-block palindromic cyclic codes (Camara-Ollivier-Tillich-type group-algebra code over Z_21, arXiv:quant-ph/0502086), n = 17..200, weight <= 8. Distance ladder: 300-trial Pauli-weight RIS screen, then 2 x 20,000 trials on fresh seeds (held). Novelty unknown: not checked against codetables.de; the dedup gate found no exact, WL-equivalent or Hadamard-image board entry. Genuinely non-CSS: a and b overlap, so every generator carries Y.",
  "references": [
   "arXiv:quant-ph/0502086"
  ],
  "novelty": "unknown"
 },
 "family": "other"
}