{
  "arxiv_id": "2605.23894",
  "title": "A Two-Branch Finite-Field Construction for Regular CSS LDPC Bases",
  "authors": ["Koki Okada", "Kenta Kasai"],
  "detailed_instance": {
    "base": {
      "J": 3,
      "L": 10,
      "field": "F16",
      "subgroup_size": 5,
      "base_length": 160,
      "rows_per_side": 48,
      "base_parameters": "[[160,76,4]]",
      "N_XZ_pairs_sharing_two": 720,
      "N6_X": 800,
      "N6_Z": 800,
      "a0": [0, 1, 2],
      "b0": [7, 3, 6],
      "a1": [8, 13, 2],
      "b1": [11, 10, 6]
    },
    "lift": {
      "type": "64-fold circulant-permutation-matrix lift",
      "P": 64,
      "length": 10240,
      "rows_per_side": 3072,
      "rank_HX": 3066,
      "rank_HZ": 3066,
      "code_parameters": "[[10240,4108,10<=d<=32]]",
      "rate": 0.401171875,
      "lift_coefficients": {
        "coefficient_count": 960,
        "html": "p64_lift_coefficients.html",
        "csv": "p64_lift_coefficients.csv",
        "json": "p64_lift_coefficients.json",
        "convention": "For side in {HX,HZ}, base edge (base_row, base_col) with shift s contributes columns base_col*64 + ((r+s) mod 64) to lifted row base_row*64 + r, for r=0,...,63."
      },
      "checks": {
        "CSS_orthogonality": "all 720 paired X-Z overlaps satisfy the zero congruence constraints",
        "same_type_6_cycles": "no same-type base 6-cycle has zero signed CPM-exponent sum",
        "weight_16_orbit": "all 20 systems for the specified two-point lift-coordinate coset support are inconsistent"
      }
    },
    "distance_certificates": {
      "lower_bound": {
        "d_X": ">=10",
        "d_Z": ">=10",
        "d": ">=10",
        "method": "complete support enumeration found no nonzero vector of weight at most 9 in either lifted kernel"
      },
      "upper_bound": {
        "d_X": "<=32",
        "d_Z": "<=32",
        "d": "<=32",
        "K": [0, 16, 32, 48],
        "A_X": [[27, 12], [37, 3], [62, 1], [72, 5], [83, 2], [93, 6], [128, 5], [138, 12]],
        "A_Z": [[64, 7], [69, 3], [74, 12], [79, 8], [81, 7], [86, 7], [91, 14], [96, 4]]
      }
    },
    "decoding_measurement": {
      "channel": "depolarizing",
      "decoder": "joint log-domain belief propagation with deterministic post-processing",
      "p": 0.058,
      "trials": 180000000,
      "recorded_failures_before_postprocessing": 25,
      "failures_after_postprocessing": 18,
      "FER_after_postprocessing": 1e-7,
      "hashing_bound_reference_for_effective_rate": 0.09403285,
      "DE_reference_for_regular_3_10": 0.0733
    }
  }
}