{
 "schema_version": "0.4",
 "name": "[[42,6,7]]",
 "code_type": "stabilizer",
 "n": 42,
 "k": 6,
 "checks": {
  "S": [
   {
    "X": [
     20,
     21,
     22,
     26,
     27,
     28
    ],
    "Z": [
     8,
     20,
     28,
     40
    ]
   },
   {
    "X": [
     21,
     22,
     23,
     27,
     28,
     29
    ],
    "Z": [
     9,
     21,
     29,
     41
    ]
   },
   {
    "X": [
     22,
     23,
     24,
     28,
     29,
     30
    ],
    "Z": [
     0,
     10,
     22,
     30
    ]
   },
   {
    "X": [
     23,
     24,
     25,
     29,
     30,
     31
    ],
    "Z": [
     1,
     11,
     23,
     31
    ]
   },
   {
    "X": [
     24,
     25,
     26,
     30,
     31,
     32
    ],
    "Z": [
     2,
     12,
     24,
     32
    ]
   },
   {
    "X": [
     25,
     26,
     27,
     31,
     32,
     33
    ],
    "Z": [
     3,
     13,
     25,
     33
    ]
   },
   {
    "X": [
     26,
     27,
     28,
     32,
     33,
     34
    ],
    "Z": [
     4,
     14,
     26,
     34
    ]
   },
   {
    "X": [
     27,
     28,
     29,
     33,
     34,
     35
    ],
    "Z": [
     5,
     15,
     27,
     35
    ]
   },
   {
    "X": [
     28,
     29,
     30,
     34,
     35,
     36
    ],
    "Z": [
     6,
     16,
     28,
     36
    ]
   },
   {
    "X": [
     29,
     30,
     31,
     35,
     36,
     37
    ],
    "Z": [
     7,
     17,
     29,
     37
    ]
   },
   {
    "X": [
     30,
     31,
     32,
     36,
     37,
     38
    ],
    "Z": [
     8,
     18,
     30,
     38
    ]
   },
   {
    "X": [
     31,
     32,
     33,
     37,
     38,
     39
    ],
    "Z": [
     9,
     19,
     31,
     39
    ]
   },
   {
    "X": [
     32,
     33,
     34,
     38,
     39,
     40
    ],
    "Z": [
     10,
     20,
     32,
     40
    ]
   },
   {
    "X": [
     33,
     34,
     35,
     39,
     40,
     41
    ],
    "Z": [
     11,
     21,
     33,
     41
    ]
   },
   {
    "X": [
     0,
     34,
     35,
     36,
     40,
     41
    ],
    "Z": [
     0,
     12,
     22,
     34
    ]
   },
   {
    "X": [
     0,
     1,
     35,
     36,
     37,
     41
    ],
    "Z": [
     1,
     13,
     23,
     35
    ]
   },
   {
    "X": [
     0,
     1,
     2,
     36,
     37,
     38
    ],
    "Z": [
     2,
     14,
     24,
     36
    ]
   },
   {
    "X": [
     1,
     2,
     3,
     37,
     38,
     39
    ],
    "Z": [
     3,
     15,
     25,
     37
    ]
   },
   {
    "X": [
     2,
     3,
     4,
     38,
     39,
     40
    ],
    "Z": [
     4,
     16,
     26,
     38
    ]
   },
   {
    "X": [
     3,
     4,
     5,
     39,
     40,
     41
    ],
    "Z": [
     5,
     17,
     27,
     39
    ]
   },
   {
    "X": [
     0,
     4,
     5,
     6,
     40,
     41
    ],
    "Z": [
     6,
     18,
     28,
     40
    ]
   },
   {
    "X": [
     0,
     1,
     5,
     6,
     7,
     41
    ],
    "Z": [
     7,
     19,
     29,
     41
    ]
   },
   {
    "X": [
     0,
     1,
     2,
     6,
     7,
     8
    ],
    "Z": [
     0,
     8,
     20,
     30
    ]
   },
   {
    "X": [
     1,
     2,
     3,
     7,
     8,
     9
    ],
    "Z": [
     1,
     9,
     21,
     31
    ]
   },
   {
    "X": [
     2,
     3,
     4,
     8,
     9,
     10
    ],
    "Z": [
     2,
     10,
     22,
     32
    ]
   },
   {
    "X": [
     3,
     4,
     5,
     9,
     10,
     11
    ],
    "Z": [
     3,
     11,
     23,
     33
    ]
   },
   {
    "X": [
     4,
     5,
     6,
     10,
     11,
     12
    ],
    "Z": [
     4,
     12,
     24,
     34
    ]
   },
   {
    "X": [
     5,
     6,
     7,
     11,
     12,
     13
    ],
    "Z": [
     5,
     13,
     25,
     35
    ]
   },
   {
    "X": [
     6,
     7,
     8,
     12,
     13,
     14
    ],
    "Z": [
     6,
     14,
     26,
     36
    ]
   },
   {
    "X": [
     7,
     8,
     9,
     13,
     14,
     15
    ],
    "Z": [
     7,
     15,
     27,
     37
    ]
   },
   {
    "X": [
     8,
     9,
     10,
     14,
     15,
     16
    ],
    "Z": [
     8,
     16,
     28,
     38
    ]
   },
   {
    "X": [
     9,
     10,
     11,
     15,
     16,
     17
    ],
    "Z": [
     9,
     17,
     29,
     39
    ]
   },
   {
    "X": [
     10,
     11,
     12,
     16,
     17,
     18
    ],
    "Z": [
     10,
     18,
     30,
     40
    ]
   },
   {
    "X": [
     11,
     12,
     13,
     17,
     18,
     19
    ],
    "Z": [
     11,
     19,
     31,
     41
    ]
   },
   {
    "X": [
     12,
     13,
     14,
     18,
     19,
     20
    ],
    "Z": [
     0,
     12,
     20,
     32
    ]
   },
   {
    "X": [
     13,
     14,
     15,
     19,
     20,
     21
    ],
    "Z": [
     1,
     13,
     21,
     33
    ]
   },
   {
    "X": [
     14,
     15,
     16,
     20,
     21,
     22
    ],
    "Z": [
     2,
     14,
     22,
     34
    ]
   },
   {
    "X": [
     15,
     16,
     17,
     21,
     22,
     23
    ],
    "Z": [
     3,
     15,
     23,
     35
    ]
   },
   {
    "X": [
     16,
     17,
     18,
     22,
     23,
     24
    ],
    "Z": [
     4,
     16,
     24,
     36
    ]
   },
   {
    "X": [
     17,
     18,
     19,
     23,
     24,
     25
    ],
    "Z": [
     5,
     17,
     25,
     37
    ]
   },
   {
    "X": [
     18,
     19,
     20,
     24,
     25,
     26
    ],
    "Z": [
     6,
     18,
     26,
     38
    ]
   },
   {
    "X": [
     19,
     20,
     21,
     25,
     26,
     27
    ],
    "Z": [
     7,
     19,
     27,
     39
    ]
   }
  ]
 },
 "distance": {
  "d": 7,
  "P": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     32,
     33,
     34
    ],
    "Z": [
     4,
     20,
     26,
     40
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "One-block cyclic stabilizer code: generator X^a Z^b and its 42 cyclic shifts, a(x) = x^20 + x^21 + x^22 + x^26 + x^27 + x^28, b(x) = x^8 + x^20 + x^28 + x^40 in F_2[x]/(x^42 - 1); a = g p, b = g q with p, q palindromic so that a b* + b a* = 0; k = deg gcd(a, b, x^42 - 1)",
  "origin": "submission",
  "date": "2026-09-30",
  "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_42, 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"
}
