{
 "schema_version": "0.4",
 "name": "[[17,1,7]] cyclic stabilizer code",
 "code_type": "stabilizer",
 "n": 17,
 "k": 1,
 "checks": {
  "S": [
   {
    "X": [
     1,
     16
    ],
    "Z": [
     3,
     5,
     6,
     11,
     12,
     14
    ]
   },
   {
    "X": [
     0,
     2
    ],
    "Z": [
     4,
     6,
     7,
     12,
     13,
     15
    ]
   },
   {
    "X": [
     1,
     3
    ],
    "Z": [
     5,
     7,
     8,
     13,
     14,
     16
    ]
   },
   {
    "X": [
     2,
     4
    ],
    "Z": [
     0,
     6,
     8,
     9,
     14,
     15
    ]
   },
   {
    "X": [
     3,
     5
    ],
    "Z": [
     1,
     7,
     9,
     10,
     15,
     16
    ]
   },
   {
    "X": [
     4,
     6
    ],
    "Z": [
     0,
     2,
     8,
     10,
     11,
     16
    ]
   },
   {
    "X": [
     5,
     7
    ],
    "Z": [
     0,
     1,
     3,
     9,
     11,
     12
    ]
   },
   {
    "X": [
     6,
     8
    ],
    "Z": [
     1,
     2,
     4,
     10,
     12,
     13
    ]
   },
   {
    "X": [
     7,
     9
    ],
    "Z": [
     2,
     3,
     5,
     11,
     13,
     14
    ]
   },
   {
    "X": [
     8,
     10
    ],
    "Z": [
     3,
     4,
     6,
     12,
     14,
     15
    ]
   },
   {
    "X": [
     9,
     11
    ],
    "Z": [
     4,
     5,
     7,
     13,
     15,
     16
    ]
   },
   {
    "X": [
     10,
     12
    ],
    "Z": [
     0,
     5,
     6,
     8,
     14,
     16
    ]
   },
   {
    "X": [
     11,
     13
    ],
    "Z": [
     0,
     1,
     6,
     7,
     9,
     15
    ]
   },
   {
    "X": [
     12,
     14
    ],
    "Z": [
     1,
     2,
     7,
     8,
     10,
     16
    ]
   },
   {
    "X": [
     13,
     15
    ],
    "Z": [
     0,
     2,
     3,
     8,
     9,
     11
    ]
   },
   {
    "X": [
     14,
     16
    ],
    "Z": [
     1,
     3,
     4,
     9,
     10,
     12
    ]
   },
   {
    "X": [
     0,
     15
    ],
    "Z": [
     2,
     4,
     5,
     10,
     11,
     13
    ]
   }
  ]
 },
 "distance": {
  "d": 7,
  "P": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     0,
     5,
     12,
     13
    ],
    "Z": [
     4,
     10,
     12,
     13,
     14
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "Cyclic stabilizer code, one-block circulant form: generator X^a Z^b with a(x) = x^1 + x^16, b(x) = x^3 + x^5 + x^6 + x^11 + x^12 + x^14 in F_2[x]/(x^17 - 1) and its n cyclic shifts; palindromic a, b make the shifts commute",
  "origin": "submission",
  "date": "2026-09-30",
  "notes": "Known parameters, new generators: the parameters are those of the cyclic (GF(4)-additive) code of Calderbank-Rains-Shor-Sloane / codetables.de at n = 17, k = 1. Generators rebuilt by exhaustive search over palindromic circulant pairs; distance 7 is exact by enumeration of all Paulis of weight < 7 (see the note); filed as upper_bound because the board's certifier does not minimise Pauli weight. Not a Hadamard image of a CSS code (generators carry X and Z on overlapping supports with k = 1 at this n); dedup gate found no match. The generators filed here are the ones our search found; equivalence to the published cyclic code was not checked, so this is a submission with known parameters, credited to CRSS for the parameters.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:quant-ph/9608006"
  ],
  "model": "Claude Fable 5.1"
 },
 "family": "other"
}