{
 "schema_version": "0.1",
 "name": "[[288,64,4]] [[4,2,2]]-amplified [[64,32,2]] 2BGA",
 "code_type": "CSS",
 "n": 288,
 "k": 64,
 "checks": {
  "X": [
   [
    0,
    20,
    128,
    148,
    232,
    252,
    272
   ],
   [
    1,
    21,
    129,
    149,
    233,
    253,
    272
   ],
   [
    2,
    22,
    130,
    150,
    234,
    254,
    272
   ],
   [
    3,
    23,
    131,
    151,
    235,
    255,
    272
   ],
   [
    76,
    116,
    180,
    204,
    228,
    244,
    273
   ],
   [
    77,
    117,
    181,
    205,
    229,
    245,
    273
   ],
   [
    78,
    118,
    182,
    206,
    230,
    246,
    273
   ],
   [
    79,
    119,
    183,
    207,
    231,
    247,
    273
   ],
   [
    68,
    112,
    172,
    196,
    224,
    240,
    274
   ],
   [
    69,
    113,
    173,
    197,
    225,
    241,
    274
   ],
   [
    70,
    114,
    174,
    198,
    226,
    242,
    274
   ],
   [
    71,
    115,
    175,
    199,
    227,
    243,
    274
   ],
   [
    64,
    108,
    168,
    192,
    220,
    236,
    275
   ],
   [
    65,
    109,
    169,
    193,
    221,
    237,
    275
   ],
   [
    66,
    110,
    170,
    194,
    222,
    238,
    275
   ],
   [
    67,
    111,
    171,
    195,
    223,
    239,
    275
   ],
   [
    104,
    124,
    216,
    232,
    248,
    252,
    276
   ],
   [
    105,
    125,
    217,
    233,
    249,
    253,
    276
   ],
   [
    106,
    126,
    218,
    234,
    250,
    254,
    276
   ],
   [
    107,
    127,
    219,
    235,
    251,
    255,
    276
   ],
   [
    52,
    100,
    180,
    196,
    228,
    240,
    277
   ],
   [
    53,
    101,
    181,
    197,
    229,
    241,
    277
   ],
   [
    54,
    102,
    182,
    198,
    230,
    242,
    277
   ],
   [
    55,
    103,
    183,
    199,
    231,
    243,
    277
   ],
   [
    44,
    96,
    160,
    172,
    212,
    224,
    278
   ],
   [
    45,
    97,
    161,
    173,
    213,
    225,
    278
   ],
   [
    46,
    98,
    162,
    174,
    214,
    226,
    278
   ],
   [
    47,
    99,
    163,
    175,
    215,
    227,
    278
   ],
   [
    40,
    92,
    156,
    168,
    208,
    220,
    279
   ],
   [
    41,
    93,
    157,
    169,
    209,
    221,
    279
   ],
   [
    42,
    94,
    158,
    170,
    210,
    222,
    279
   ],
   [
    43,
    95,
    159,
    171,
    211,
    223,
    279
   ],
   [
    88,
    120,
    204,
    216,
    244,
    248,
    280
   ],
   [
    89,
    121,
    205,
    217,
    245,
    249,
    280
   ],
   [
    90,
    122,
    206,
    218,
    246,
    250,
    280
   ],
   [
    91,
    123,
    207,
    219,
    247,
    251,
    280
   ],
   [
    32,
    84,
    144,
    160,
    188,
    212,
    281
   ],
   [
    33,
    85,
    145,
    161,
    189,
    213,
    281
   ],
   [
    34,
    86,
    146,
    162,
    190,
    214,
    281
   ],
   [
    35,
    87,
    147,
    163,
    191,
    215,
    281
   ],
   [
    28,
    80,
    140,
    156,
    184,
    208,
    282
   ],
   [
    29,
    81,
    141,
    157,
    185,
    209,
    282
   ],
   [
    30,
    82,
    142,
    158,
    186,
    210,
    282
   ],
   [
    31,
    83,
    143,
    159,
    187,
    211,
    282
   ],
   [
    24,
    72,
    136,
    152,
    176,
    200,
    283
   ],
   [
    25,
    73,
    137,
    153,
    177,
    201,
    283
   ],
   [
    26,
    74,
    138,
    154,
    178,
    202,
    283
   ],
   [
    27,
    75,
    139,
    155,
    179,
    203,
    283
   ],
   [
    16,
    60,
    144,
    188,
    192,
    236,
    284
   ],
   [
    17,
    61,
    145,
    189,
    193,
    237,
    284
   ],
   [
    18,
    62,
    146,
    190,
    194,
    238,
    284
   ],
   [
    19,
    63,
    147,
    191,
    195,
    239,
    284
   ],
   [
    12,
    56,
    140,
    152,
    184,
    200,
    285
   ],
   [
    13,
    57,
    141,
    153,
    185,
    201,
    285
   ],
   [
    14,
    58,
    142,
    154,
    186,
    202,
    285
   ],
   [
    15,
    59,
    143,
    155,
    187,
    203,
    285
   ],
   [
    8,
    48,
    132,
    136,
    164,
    176,
    286
   ],
   [
    9,
    49,
    133,
    137,
    165,
    177,
    286
   ],
   [
    10,
    50,
    134,
    138,
    166,
    178,
    286
   ],
   [
    11,
    51,
    135,
    139,
    167,
    179,
    286
   ],
   [
    4,
    36,
    128,
    132,
    148,
    164,
    287
   ],
   [
    5,
    37,
    129,
    133,
    149,
    165,
    287
   ],
   [
    6,
    38,
    130,
    134,
    150,
    166,
    287
   ],
   [
    7,
    39,
    131,
    135,
    151,
    167,
    287
   ],
   [
    0,
    1,
    2,
    3,
    256,
    260
   ],
   [
    4,
    5,
    6,
    7,
    256,
    271
   ],
   [
    8,
    9,
    10,
    11,
    270,
    271
   ],
   [
    12,
    13,
    14,
    15,
    267,
    269
   ],
   [
    16,
    17,
    18,
    19,
    259,
    268
   ],
   [
    20,
    21,
    22,
    23,
    256,
    260
   ],
   [
    24,
    25,
    26,
    27,
    267,
    270
   ],
   [
    28,
    29,
    30,
    31,
    266,
    269
   ],
   [
    32,
    33,
    34,
    35,
    265,
    268
   ],
   [
    36,
    37,
    38,
    39,
    256,
    271
   ],
   [
    40,
    41,
    42,
    43,
    263,
    266
   ],
   [
    44,
    45,
    46,
    47,
    262,
    265
   ],
   [
    48,
    49,
    50,
    51,
    270,
    271
   ],
   [
    52,
    53,
    54,
    55,
    258,
    261
   ],
   [
    56,
    57,
    58,
    59,
    267,
    269
   ],
   [
    60,
    61,
    62,
    63,
    259,
    268
   ],
   [
    64,
    65,
    66,
    67,
    259,
    263
   ],
   [
    68,
    69,
    70,
    71,
    258,
    262
   ],
   [
    72,
    73,
    74,
    75,
    267,
    270
   ],
   [
    76,
    77,
    78,
    79,
    257,
    261
   ],
   [
    80,
    81,
    82,
    83,
    266,
    269
   ],
   [
    84,
    85,
    86,
    87,
    265,
    268
   ],
   [
    88,
    89,
    90,
    91,
    257,
    264
   ],
   [
    92,
    93,
    94,
    95,
    263,
    266
   ],
   [
    96,
    97,
    98,
    99,
    262,
    265
   ],
   [
    100,
    101,
    102,
    103,
    258,
    261
   ],
   [
    104,
    105,
    106,
    107,
    260,
    264
   ],
   [
    108,
    109,
    110,
    111,
    259,
    263
   ],
   [
    112,
    113,
    114,
    115,
    258,
    262
   ],
   [
    116,
    117,
    118,
    119,
    257,
    261
   ],
   [
    120,
    121,
    122,
    123,
    257,
    264
   ],
   [
    124,
    125,
    126,
    127,
    260,
    264
   ],
   [
    128,
    129,
    130,
    131,
    256
   ],
   [
    132,
    133,
    134,
    135,
    271
   ],
   [
    136,
    137,
    138,
    139,
    270
   ],
   [
    140,
    141,
    142,
    143,
    269
   ],
   [
    144,
    145,
    146,
    147,
    268
   ],
   [
    148,
    149,
    150,
    151,
    256
   ],
   [
    152,
    153,
    154,
    155,
    267
   ],
   [
    156,
    157,
    158,
    159,
    266
   ],
   [
    160,
    161,
    162,
    163,
    265
   ],
   [
    164,
    165,
    166,
    167,
    271
   ],
   [
    168,
    169,
    170,
    171,
    263
   ],
   [
    172,
    173,
    174,
    175,
    262
   ],
   [
    176,
    177,
    178,
    179,
    270
   ],
   [
    180,
    181,
    182,
    183,
    261
   ],
   [
    184,
    185,
    186,
    187,
    269
   ],
   [
    188,
    189,
    190,
    191,
    268
   ],
   [
    192,
    193,
    194,
    195,
    259
   ],
   [
    196,
    197,
    198,
    199,
    258
   ],
   [
    200,
    201,
    202,
    203,
    267
   ],
   [
    204,
    205,
    206,
    207,
    257
   ],
   [
    208,
    209,
    210,
    211,
    266
   ],
   [
    212,
    213,
    214,
    215,
    265
   ],
   [
    216,
    217,
    218,
    219,
    264
   ],
   [
    220,
    221,
    222,
    223,
    263
   ],
   [
    224,
    225,
    226,
    227,
    262
   ],
   [
    228,
    229,
    230,
    231,
    261
   ],
   [
    232,
    233,
    234,
    235,
    260
   ],
   [
    236,
    237,
    238,
    239,
    259
   ],
   [
    240,
    241,
    242,
    243,
    258
   ],
   [
    244,
    245,
    246,
    247,
    257
   ],
   [
    248,
    249,
    250,
    251,
    264
   ],
   [
    252,
    253,
    254,
    255,
    260
   ]
  ],
  "Z": [
   [
    0,
    4,
    20,
    36,
    128,
    148,
    256
   ],
   [
    1,
    5,
    21,
    37,
    129,
    149,
    256
   ],
   [
    2,
    6,
    22,
    38,
    130,
    150,
    256
   ],
   [
    3,
    7,
    23,
    39,
    131,
    151,
    256
   ],
   [
    76,
    88,
    116,
    120,
    204,
    244,
    257
   ],
   [
    77,
    89,
    117,
    121,
    205,
    245,
    257
   ],
   [
    78,
    90,
    118,
    122,
    206,
    246,
    257
   ],
   [
    79,
    91,
    119,
    123,
    207,
    247,
    257
   ],
   [
    52,
    68,
    100,
    112,
    196,
    240,
    258
   ],
   [
    53,
    69,
    101,
    113,
    197,
    241,
    258
   ],
   [
    54,
    70,
    102,
    114,
    198,
    242,
    258
   ],
   [
    55,
    71,
    103,
    115,
    199,
    243,
    258
   ],
   [
    16,
    60,
    64,
    108,
    192,
    236,
    259
   ],
   [
    17,
    61,
    65,
    109,
    193,
    237,
    259
   ],
   [
    18,
    62,
    66,
    110,
    194,
    238,
    259
   ],
   [
    19,
    63,
    67,
    111,
    195,
    239,
    259
   ],
   [
    0,
    20,
    104,
    124,
    232,
    252,
    260
   ],
   [
    1,
    21,
    105,
    125,
    233,
    253,
    260
   ],
   [
    2,
    22,
    106,
    126,
    234,
    254,
    260
   ],
   [
    3,
    23,
    107,
    127,
    235,
    255,
    260
   ],
   [
    52,
    76,
    100,
    116,
    180,
    228,
    261
   ],
   [
    53,
    77,
    101,
    117,
    181,
    229,
    261
   ],
   [
    54,
    78,
    102,
    118,
    182,
    230,
    261
   ],
   [
    55,
    79,
    103,
    119,
    183,
    231,
    261
   ],
   [
    44,
    68,
    96,
    112,
    172,
    224,
    262
   ],
   [
    45,
    69,
    97,
    113,
    173,
    225,
    262
   ],
   [
    46,
    70,
    98,
    114,
    174,
    226,
    262
   ],
   [
    47,
    71,
    99,
    115,
    175,
    227,
    262
   ],
   [
    40,
    64,
    92,
    108,
    168,
    220,
    263
   ],
   [
    41,
    65,
    93,
    109,
    169,
    221,
    263
   ],
   [
    42,
    66,
    94,
    110,
    170,
    222,
    263
   ],
   [
    43,
    67,
    95,
    111,
    171,
    223,
    263
   ],
   [
    88,
    104,
    120,
    124,
    216,
    248,
    264
   ],
   [
    89,
    105,
    121,
    125,
    217,
    249,
    264
   ],
   [
    90,
    106,
    122,
    126,
    218,
    250,
    264
   ],
   [
    91,
    107,
    123,
    127,
    219,
    251,
    264
   ],
   [
    32,
    44,
    84,
    96,
    160,
    212,
    265
   ],
   [
    33,
    45,
    85,
    97,
    161,
    213,
    265
   ],
   [
    34,
    46,
    86,
    98,
    162,
    214,
    265
   ],
   [
    35,
    47,
    87,
    99,
    163,
    215,
    265
   ],
   [
    28,
    40,
    80,
    92,
    156,
    208,
    266
   ],
   [
    29,
    41,
    81,
    93,
    157,
    209,
    266
   ],
   [
    30,
    42,
    82,
    94,
    158,
    210,
    266
   ],
   [
    31,
    43,
    83,
    95,
    159,
    211,
    266
   ],
   [
    12,
    24,
    56,
    72,
    152,
    200,
    267
   ],
   [
    13,
    25,
    57,
    73,
    153,
    201,
    267
   ],
   [
    14,
    26,
    58,
    74,
    154,
    202,
    267
   ],
   [
    15,
    27,
    59,
    75,
    155,
    203,
    267
   ],
   [
    16,
    32,
    60,
    84,
    144,
    188,
    268
   ],
   [
    17,
    33,
    61,
    85,
    145,
    189,
    268
   ],
   [
    18,
    34,
    62,
    86,
    146,
    190,
    268
   ],
   [
    19,
    35,
    63,
    87,
    147,
    191,
    268
   ],
   [
    12,
    28,
    56,
    80,
    140,
    184,
    269
   ],
   [
    13,
    29,
    57,
    81,
    141,
    185,
    269
   ],
   [
    14,
    30,
    58,
    82,
    142,
    186,
    269
   ],
   [
    15,
    31,
    59,
    83,
    143,
    187,
    269
   ],
   [
    8,
    24,
    48,
    72,
    136,
    176,
    270
   ],
   [
    9,
    25,
    49,
    73,
    137,
    177,
    270
   ],
   [
    10,
    26,
    50,
    74,
    138,
    178,
    270
   ],
   [
    11,
    27,
    51,
    75,
    139,
    179,
    270
   ],
   [
    4,
    8,
    36,
    48,
    132,
    164,
    271
   ],
   [
    5,
    9,
    37,
    49,
    133,
    165,
    271
   ],
   [
    6,
    10,
    38,
    50,
    134,
    166,
    271
   ],
   [
    7,
    11,
    39,
    51,
    135,
    167,
    271
   ],
   [
    0,
    1,
    2,
    3,
    272
   ],
   [
    4,
    5,
    6,
    7,
    287
   ],
   [
    8,
    9,
    10,
    11,
    286
   ],
   [
    12,
    13,
    14,
    15,
    285
   ],
   [
    16,
    17,
    18,
    19,
    284
   ],
   [
    20,
    21,
    22,
    23,
    272
   ],
   [
    24,
    25,
    26,
    27,
    283
   ],
   [
    28,
    29,
    30,
    31,
    282
   ],
   [
    32,
    33,
    34,
    35,
    281
   ],
   [
    36,
    37,
    38,
    39,
    287
   ],
   [
    40,
    41,
    42,
    43,
    279
   ],
   [
    44,
    45,
    46,
    47,
    278
   ],
   [
    48,
    49,
    50,
    51,
    286
   ],
   [
    52,
    53,
    54,
    55,
    277
   ],
   [
    56,
    57,
    58,
    59,
    285
   ],
   [
    60,
    61,
    62,
    63,
    284
   ],
   [
    64,
    65,
    66,
    67,
    275
   ],
   [
    68,
    69,
    70,
    71,
    274
   ],
   [
    72,
    73,
    74,
    75,
    283
   ],
   [
    76,
    77,
    78,
    79,
    273
   ],
   [
    80,
    81,
    82,
    83,
    282
   ],
   [
    84,
    85,
    86,
    87,
    281
   ],
   [
    88,
    89,
    90,
    91,
    280
   ],
   [
    92,
    93,
    94,
    95,
    279
   ],
   [
    96,
    97,
    98,
    99,
    278
   ],
   [
    100,
    101,
    102,
    103,
    277
   ],
   [
    104,
    105,
    106,
    107,
    276
   ],
   [
    108,
    109,
    110,
    111,
    275
   ],
   [
    112,
    113,
    114,
    115,
    274
   ],
   [
    116,
    117,
    118,
    119,
    273
   ],
   [
    120,
    121,
    122,
    123,
    280
   ],
   [
    124,
    125,
    126,
    127,
    276
   ],
   [
    128,
    129,
    130,
    131,
    272,
    287
   ],
   [
    132,
    133,
    134,
    135,
    286,
    287
   ],
   [
    136,
    137,
    138,
    139,
    283,
    286
   ],
   [
    140,
    141,
    142,
    143,
    282,
    285
   ],
   [
    144,
    145,
    146,
    147,
    281,
    284
   ],
   [
    148,
    149,
    150,
    151,
    272,
    287
   ],
   [
    152,
    153,
    154,
    155,
    283,
    285
   ],
   [
    156,
    157,
    158,
    159,
    279,
    282
   ],
   [
    160,
    161,
    162,
    163,
    278,
    281
   ],
   [
    164,
    165,
    166,
    167,
    286,
    287
   ],
   [
    168,
    169,
    170,
    171,
    275,
    279
   ],
   [
    172,
    173,
    174,
    175,
    274,
    278
   ],
   [
    176,
    177,
    178,
    179,
    283,
    286
   ],
   [
    180,
    181,
    182,
    183,
    273,
    277
   ],
   [
    184,
    185,
    186,
    187,
    282,
    285
   ],
   [
    188,
    189,
    190,
    191,
    281,
    284
   ],
   [
    192,
    193,
    194,
    195,
    275,
    284
   ],
   [
    196,
    197,
    198,
    199,
    274,
    277
   ],
   [
    200,
    201,
    202,
    203,
    283,
    285
   ],
   [
    204,
    205,
    206,
    207,
    273,
    280
   ],
   [
    208,
    209,
    210,
    211,
    279,
    282
   ],
   [
    212,
    213,
    214,
    215,
    278,
    281
   ],
   [
    216,
    217,
    218,
    219,
    276,
    280
   ],
   [
    220,
    221,
    222,
    223,
    275,
    279
   ],
   [
    224,
    225,
    226,
    227,
    274,
    278
   ],
   [
    228,
    229,
    230,
    231,
    273,
    277
   ],
   [
    232,
    233,
    234,
    235,
    272,
    276
   ],
   [
    236,
    237,
    238,
    239,
    275,
    284
   ],
   [
    240,
    241,
    242,
    243,
    274,
    277
   ],
   [
    244,
    245,
    246,
    247,
    273,
    280
   ],
   [
    248,
    249,
    250,
    251,
    276,
    280
   ],
   [
    252,
    253,
    254,
    255,
    272,
    276
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    44,
    45,
    96,
    97
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    32,
    33,
    84,
    85
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Distance-amplified code: one [[4,2,2]] tensor-product amplification step (central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[64,32,2]] 2BGA entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 288, k' = 2k = 64, check weight w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 4/4); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 4). Base provenance: 2BGA (arXiv:2306.16400) on SmallGroup(32,1), from github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c, abelian.zip, diswtabelian_wt6wtL2_order32_k32.txt, line 1. nonidentity supports a=[6], b=[2, 6, 10].",
  "references": [
   "arXiv:2609.37231"
  ],
  "date": "2026-09-30",
  "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model.",
  "model": "Space Bunny Alpha 1.0"
 },
 "family": "distance-amplified"
}
