files / problems / covering / compute / q12 / certificate.json

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{
  "seed": {
    "r": 12,
    "n": 37,
    "rank": 12,
    "covering_radius": 3,
    "covered_le0_to_le3": [
      1,
      38,
      591,
      4096
    ],
    "nonempty_zero_representations_le3": 0
  },
  "unique_representation_conflict_edges": 466,
  "forced_singletons_one_based": [
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    27,
    29,
    30,
    31,
    35
  ],
  "obstruction_syndrome_lsb_integer": 277,
  "all_obstruction_representations_one_based": [
    [
      1,
      13,
      15
    ],
    [
      2,
      15,
      37
    ],
    [
      14,
      17,
      23
    ],
    [
      15,
      18,
      26
    ],
    [
      18,
      20,
      33
    ],
    [
      18,
      22,
      28
    ],
    [
      21,
      23,
      24
    ],
    [
      21,
      34,
      36
    ],
    [
      23,
      32,
      36
    ],
    [
      24,
      32,
      34
    ]
  ],
  "ell0_minimum_blocks": 18,
  "ell1_ell2_ell3": "impossible for every block count: syndrome zero",
  "partition_p18_one_based": [
    [
      3
    ],
    [
      4
    ],
    [
      5
    ],
    [
      6
    ],
    [
      7
    ],
    [
      8
    ],
    [
      9
    ],
    [
      10
    ],
    [
      11
    ],
    [
      12
    ],
    [
      27
    ],
    [
      29
    ],
    [
      30
    ],
    [
      31
    ],
    [
      35
    ],
    [
      1,
      2,
      16,
      20,
      21,
      23,
      34
    ],
    [
      14,
      17,
      18,
      24,
      26,
      32,
      36,
      37
    ],
    [
      13,
      15,
      19,
      22,
      25,
      28,
      33
    ]
  ],
  "at_m4_indicator_capacity": 17,
  "target_length_not_constructed": 607,
  "published_length_arxiv_2511_02542v1_table7_1_r24": 618
}