{
  "instance": "qc_472_122_14",
  "M": [
    [
      [
        [
          0,
          5
        ],
        [
          1,
          7
        ],
        [
          2,
          4
        ],
        [
          3,
          6
        ]
      ],
      [
        [
          0,
          4
        ],
        [
          1,
          5
        ],
        [
          2,
          6
        ],
        [
          3,
          7
        ]
      ],
      [
        [
          0,
          7
        ],
        [
          1,
          6
        ],
        [
          2,
          5
        ],
        [
          3,
          4
        ]
      ]
    ],
    [
      [
        [
          0,
          7
        ],
        [
          1,
          6
        ],
        [
          2,
          5
        ],
        [
          3,
          4
        ]
      ],
      [
        [
          0,
          5
        ],
        [
          1,
          7
        ],
        [
          2,
          4
        ],
        [
          3,
          6
        ]
      ],
      [
        [
          0,
          4
        ],
        [
          1,
          5
        ],
        [
          2,
          6
        ],
        [
          3,
          7
        ]
      ]
    ],
    [
      [
        [
          0,
          4
        ],
        [
          1,
          5
        ],
        [
          2,
          6
        ],
        [
          3,
          7
        ]
      ],
      [
        [
          0,
          7
        ],
        [
          1,
          6
        ],
        [
          2,
          5
        ],
        [
          3,
          4
        ]
      ],
      [
        [
          0,
          5
        ],
        [
          1,
          7
        ],
        [
          2,
          4
        ],
        [
          3,
          6
        ]
      ]
    ]
  ],
  "E": [
    [
      53,
      43,
      36,
      43,
      56,
      44,
      49,
      9
    ],
    [
      56,
      8,
      52,
      24,
      2,
      45,
      29,
      47
    ],
    [
      5,
      14,
      44,
      22,
      23,
      39,
      33,
      32
    ]
  ],
  "D": [
    [
      11,
      36,
      9,
      51,
      29,
      2,
      57,
      2
    ],
    [
      9,
      56,
      3,
      11,
      12,
      57,
      16,
      36
    ],
    [
      51,
      48,
      18,
      43,
      56,
      26,
      54,
      7
    ]
  ],
  "parameters": {
    "M_rows": 3,
    "J": 3,
    "L": 8,
    "P": 59,
    "g": 6,
    "n": 472,
    "k": 122,
    "d": 14,
    "instance": "qc_472_122_14"
  },
  "checks": {
    "css_orthogonal": true,
    "Hx_no_4cycles": true,
    "Hz_no_4cycles": true,
    "Hx_row_weight_histogram": {
      "8": 177
    },
    "Hz_row_weight_histogram": {
      "8": 177
    },
    "Hx_column_weight_histogram": {
      "3": 472
    },
    "Hz_column_weight_histogram": {
      "3": 472
    },
    "girth_Hx": 6,
    "girth_Hz": 6,
    "rank_Hx": 175,
    "rank_Hz": 175,
    "k": 122,
    "Hx_check_intersection_triangles": 649,
    "Hz_check_intersection_triangles": 649
  },
  "non_permutation_equivalence_certificate": "check-intersection triangle count differs.  The recorded quantity is invariant under row permutations of X checks, row permutations of Z checks, and common column permutations.",
  "distance_verification": {
    "X": {
      "complete": true,
      "found": false,
      "max_weight_searched_for_lower_bound": 12,
      "upper_found": true,
      "upper_weight": 14
    },
    "Z": {
      "complete": true,
      "found": false,
      "max_weight_searched_for_lower_bound": 12,
      "upper_found": true,
      "upper_weight": 14
    },
    "even_kernel_parity_used": true,
    "lower_bound_reason": "complete exclusion through weight 12, plus even-weight kernel parity",
    "certifies_lower_bound": true,
    "certifies_exact_distance": true
  },
  "source_candidate_id": "qc_472_122_14",
  "prepublication_search_candidate_id": "qc_472_l8_p59_candidate_0020"
}