{
  "arxiv_id": "2604.20838",
  "title": "High-Girth Regular Quantum LDPC Codes from Affine-Coset Structures",
  "authors": ["Koki Okada", "Kenta Kasai"],
  "software_repository": "https://github.com/kasaikenta/quantum-ldpc-decoder",
  "detailed_instance": {
    "base": {
      "type": "affine-coset CSS base, permutation-equivalent to the SPC(3) product CSS code",
      "regularity": "(3,8)",
      "base_length": 512,
      "rows_per_side": 192,
      "row_weight": 8,
      "column_weight": 3,
      "tanner_girth_X": 8,
      "tanner_girth_Z": 8,
      "base_parameters": "[[512,174,8]]"
    },
    "lift": {
      "type": "32-fold circulant-permutation-matrix lift",
      "P": 32,
      "length": 16384,
      "rows_per_side": 6144,
      "rank_HX": 6121,
      "rank_HZ": 6121,
      "code_parameters": "[[16384,4142,<=40]]",
      "rate": 0.2528076171875,
      "row_weight": 8,
      "column_weight": 3,
      "lift_coefficients": {
        "coefficient_count": 3072,
        "html": "p32_lift_coefficients.html",
        "csv": "p32_lift_coefficients.csv",
        "json": "p32_lift_coefficients.json",
        "original_csv": "cpm_labels.csv",
        "convention": "For side in {HX,HZ}, base edge (base_row, base_col) with shift s contributes columns base_col*32 + ((r+s) mod 32) to lifted row base_row*32 + r, for r=0,...,31."
      },
      "matrix_files": {
        "HX_matrix_market": "cpm_HX.mtx",
        "HZ_matrix_market": "cpm_HZ.mtx"
      },
      "cycle_summary": {
        "base_x_8cycles": 18816,
        "base_z_8cycles": 18816,
        "cpm_zero_voltage_x_cycles": 1466,
        "cpm_zero_voltage_z_cycles": 1491,
        "cpm_lifted_8cycles_x": 46912,
        "cpm_lifted_8cycles_z": 47712
      }
    },
    "distance_certificate": {
      "upper_bound": {
        "d": "<=40",
        "method": "one observed syndrome-satisfying non-stabilizer logical residual of Pauli weight 40 in the decoding experiment"
      },
      "note": "The paper reports this as a decoder-derived upper bound, not an exact distance claim."
    },
    "decoding_measurement": {
      "channel": "code-capacity depolarizing",
      "decoder": "belief propagation with post-processing",
      "p": 0.085,
      "trials": 2310469200,
      "final_failures": 23,
      "syndrome_satisfying_logical_failures": 1,
      "residual_syndrome_failures": 22,
      "FER": 9.95468798148774e-9,
      "DE_reference_for_regular_3_8": 0.1009
    }
  }
}