files / problems / covering / share / 2026-08-16 / result / data / partition_p10.json

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{
 "_schema": "columns[i] is the LSB-first integer encoding of column i of data/H_r10_n50.txt (bit k = row k+1); block_of_column[i] is the index of the block containing that column. The blocks form a (2,0)-partition in the sense of arXiv:2511.02542 Definition 3.2: every element of F_2^10, including 0, is a sum of at most two columns drawn from distinct blocks. Verified by verify/verify.py --partition and by verify/verify.rs.",
 "block_of_column": [
  4,
  0,
  6,
  5,
  6,
  9,
  4,
  1,
  0,
  5,
  3,
  0,
  0,
  4,
  4,
  3,
  4,
  5,
  9,
  5,
  9,
  2,
  6,
  8,
  4,
  5,
  7,
  6,
  4,
  5,
  9,
  9,
  5,
  4,
  6,
  6,
  0,
  9,
  9,
  9,
  5,
  0,
  6,
  6,
  2,
  0,
  9,
  0,
  2,
  7
 ],
 "block_sizes": [
  8,
  1,
  3,
  2,
  8,
  8,
  8,
  2,
  1,
  9
 ],
 "blocks": {
  "0": [
   2,
   128,
   202,
   212,
   771,
   855,
   897,
   981
  ],
  "1": [
   86
  ],
  "2": [
   381,
   893,
   1003
  ],
  "3": [
   183,
   297
  ],
  "4": [
   1,
   65,
   247,
   256,
   320,
   438,
   502,
   734
  ],
  "5": [
   15,
   173,
   329,
   366,
   460,
   559,
   653,
   846
  ],
  "6": [
   4,
   16,
   391,
   491,
   742,
   754,
   869,
   881
  ],
  "7": [
   479,
   1004
  ],
  "8": [
   403
  ],
  "9": [
   32,
   341,
   373,
   576,
   608,
   777,
   789,
   821,
   927
  ]
 },
 "columns": [
  1,
  2,
  4,
  15,
  16,
  32,
  65,
  86,
  128,
  173,
  183,
  202,
  212,
  247,
  256,
  297,
  320,
  329,
  341,
  366,
  373,
  381,
  391,
  403,
  438,
  460,
  479,
  491,
  502,
  559,
  576,
  608,
  653,
  734,
  742,
  754,
  771,
  777,
  789,
  821,
  846,
  855,
  869,
  881,
  893,
  897,
  927,
  981,
  1003,
  1004
 ],
 "length": 50,
 "p_H": 10,
 "redundancy": 10,
 "source_matrix": "data/H_r10_n50.txt"
}