{
 "schema_version": "0.3",
 "name": "Cornucopia [[288,148,6]]",
 "code_type": "CSS",
 "n": 288,
 "k": 148,
 "checks": {
  "X": [
   [
    12,
    45,
    52,
    79,
    101,
    121,
    148,
    170,
    204,
    234,
    247,
    271
   ],
   [
    13,
    46,
    53,
    72,
    102,
    122,
    149,
    171,
    205,
    235,
    240,
    264
   ],
   [
    14,
    47,
    54,
    73,
    103,
    123,
    150,
    172,
    206,
    236,
    241,
    265
   ],
   [
    15,
    40,
    55,
    74,
    96,
    124,
    151,
    173,
    207,
    237,
    242,
    266
   ],
   [
    8,
    41,
    48,
    75,
    97,
    125,
    144,
    174,
    200,
    238,
    243,
    267
   ],
   [
    9,
    42,
    49,
    76,
    98,
    126,
    145,
    175,
    201,
    239,
    244,
    268
   ],
   [
    10,
    43,
    50,
    77,
    99,
    127,
    146,
    168,
    202,
    232,
    245,
    269
   ],
   [
    11,
    44,
    51,
    78,
    100,
    120,
    147,
    169,
    203,
    233,
    246,
    270
   ],
   [
    20,
    37,
    60,
    87,
    109,
    129,
    156,
    178,
    212,
    226,
    255,
    279
   ],
   [
    21,
    38,
    61,
    80,
    110,
    130,
    157,
    179,
    213,
    227,
    248,
    272
   ],
   [
    22,
    39,
    62,
    81,
    111,
    131,
    158,
    180,
    214,
    228,
    249,
    273
   ],
   [
    23,
    32,
    63,
    82,
    104,
    132,
    159,
    181,
    215,
    229,
    250,
    274
   ],
   [
    16,
    33,
    56,
    83,
    105,
    133,
    152,
    182,
    208,
    230,
    251,
    275
   ],
   [
    17,
    34,
    57,
    84,
    106,
    134,
    153,
    183,
    209,
    231,
    252,
    276
   ],
   [
    18,
    35,
    58,
    85,
    107,
    135,
    154,
    176,
    210,
    224,
    253,
    277
   ],
   [
    19,
    36,
    59,
    86,
    108,
    128,
    155,
    177,
    211,
    225,
    254,
    278
   ],
   [
    4,
    29,
    68,
    95,
    117,
    137,
    164,
    186,
    196,
    218,
    263,
    287
   ],
   [
    5,
    30,
    69,
    88,
    118,
    138,
    165,
    187,
    197,
    219,
    256,
    280
   ],
   [
    6,
    31,
    70,
    89,
    119,
    139,
    166,
    188,
    198,
    220,
    257,
    281
   ],
   [
    7,
    24,
    71,
    90,
    112,
    140,
    167,
    189,
    199,
    221,
    258,
    282
   ],
   [
    0,
    25,
    64,
    91,
    113,
    141,
    160,
    190,
    192,
    222,
    259,
    283
   ],
   [
    1,
    26,
    65,
    92,
    114,
    142,
    161,
    191,
    193,
    223,
    260,
    284
   ],
   [
    2,
    27,
    66,
    93,
    115,
    143,
    162,
    184,
    194,
    216,
    261,
    285
   ],
   [
    3,
    28,
    67,
    94,
    116,
    136,
    163,
    185,
    195,
    217,
    262,
    286
   ],
   [
    1,
    36,
    69,
    76,
    103,
    125,
    151,
    172,
    194,
    228,
    258,
    271
   ],
   [
    2,
    37,
    70,
    77,
    96,
    126,
    144,
    173,
    195,
    229,
    259,
    264
   ],
   [
    3,
    38,
    71,
    78,
    97,
    127,
    145,
    174,
    196,
    230,
    260,
    265
   ],
   [
    4,
    39,
    64,
    79,
    98,
    120,
    146,
    175,
    197,
    231,
    261,
    266
   ],
   [
    5,
    32,
    65,
    72,
    99,
    121,
    147,
    168,
    198,
    224,
    262,
    267
   ],
   [
    6,
    33,
    66,
    73,
    100,
    122,
    148,
    169,
    199,
    225,
    263,
    268
   ],
   [
    7,
    34,
    67,
    74,
    101,
    123,
    149,
    170,
    192,
    226,
    256,
    269
   ],
   [
    0,
    35,
    68,
    75,
    102,
    124,
    150,
    171,
    193,
    227,
    257,
    270
   ],
   [
    9,
    44,
    61,
    84,
    111,
    133,
    159,
    180,
    202,
    236,
    250,
    279
   ],
   [
    10,
    45,
    62,
    85,
    104,
    134,
    152,
    181,
    203,
    237,
    251,
    272
   ],
   [
    11,
    46,
    63,
    86,
    105,
    135,
    153,
    182,
    204,
    238,
    252,
    273
   ],
   [
    12,
    47,
    56,
    87,
    106,
    128,
    154,
    183,
    205,
    239,
    253,
    274
   ],
   [
    13,
    40,
    57,
    80,
    107,
    129,
    155,
    176,
    206,
    232,
    254,
    275
   ],
   [
    14,
    41,
    58,
    81,
    108,
    130,
    156,
    177,
    207,
    233,
    255,
    276
   ],
   [
    15,
    42,
    59,
    82,
    109,
    131,
    157,
    178,
    200,
    234,
    248,
    277
   ],
   [
    8,
    43,
    60,
    83,
    110,
    132,
    158,
    179,
    201,
    235,
    249,
    278
   ],
   [
    17,
    28,
    53,
    92,
    119,
    141,
    167,
    188,
    210,
    220,
    242,
    287
   ],
   [
    18,
    29,
    54,
    93,
    112,
    142,
    160,
    189,
    211,
    221,
    243,
    280
   ],
   [
    19,
    30,
    55,
    94,
    113,
    143,
    161,
    190,
    212,
    222,
    244,
    281
   ],
   [
    20,
    31,
    48,
    95,
    114,
    136,
    162,
    191,
    213,
    223,
    245,
    282
   ],
   [
    21,
    24,
    49,
    88,
    115,
    137,
    163,
    184,
    214,
    216,
    246,
    283
   ],
   [
    22,
    25,
    50,
    89,
    116,
    138,
    164,
    185,
    215,
    217,
    247,
    284
   ],
   [
    23,
    26,
    51,
    90,
    117,
    139,
    165,
    186,
    208,
    218,
    240,
    285
   ],
   [
    16,
    27,
    52,
    91,
    118,
    140,
    166,
    187,
    209,
    219,
    241,
    286
   ],
   [
    5,
    25,
    60,
    93,
    100,
    127,
    151,
    175,
    196,
    218,
    252,
    282
   ],
   [
    6,
    26,
    61,
    94,
    101,
    120,
    144,
    168,
    197,
    219,
    253,
    283
   ],
   [
    7,
    27,
    62,
    95,
    102,
    121,
    145,
    169,
    198,
    220,
    254,
    284
   ],
   [
    0,
    28,
    63,
    88,
    103,
    122,
    146,
    170,
    199,
    221,
    255,
    285
   ],
   [
    1,
    29,
    56,
    89,
    96,
    123,
    147,
    171,
    192,
    222,
    248,
    286
   ],
   [
    2,
    30,
    57,
    90,
    97,
    124,
    148,
    172,
    193,
    223,
    249,
    287
   ],
   [
    3,
    31,
    58,
    91,
    98,
    125,
    149,
    173,
    194,
    216,
    250,
    280
   ],
   [
    4,
    24,
    59,
    92,
    99,
    126,
    150,
    174,
    195,
    217,
    251,
    281
   ],
   [
    13,
    33,
    68,
    85,
    108,
    135,
    159,
    183,
    204,
    226,
    260,
    274
   ],
   [
    14,
    34,
    69,
    86,
    109,
    128,
    152,
    176,
    205,
    227,
    261,
    275
   ],
   [
    15,
    35,
    70,
    87,
    110,
    129,
    153,
    177,
    206,
    228,
    262,
    276
   ],
   [
    8,
    36,
    71,
    80,
    111,
    130,
    154,
    178,
    207,
    229,
    263,
    277
   ],
   [
    9,
    37,
    64,
    81,
    104,
    131,
    155,
    179,
    200,
    230,
    256,
    278
   ],
   [
    10,
    38,
    65,
    82,
    105,
    132,
    156,
    180,
    201,
    231,
    257,
    279
   ],
   [
    11,
    39,
    66,
    83,
    106,
    133,
    157,
    181,
    202,
    224,
    258,
    272
   ],
   [
    12,
    32,
    67,
    84,
    107,
    134,
    158,
    182,
    203,
    225,
    259,
    273
   ],
   [
    21,
    41,
    52,
    77,
    116,
    143,
    167,
    191,
    212,
    234,
    244,
    266
   ],
   [
    22,
    42,
    53,
    78,
    117,
    136,
    160,
    184,
    213,
    235,
    245,
    267
   ],
   [
    23,
    43,
    54,
    79,
    118,
    137,
    161,
    185,
    214,
    236,
    246,
    268
   ],
   [
    16,
    44,
    55,
    72,
    119,
    138,
    162,
    186,
    215,
    237,
    247,
    269
   ],
   [
    17,
    45,
    48,
    73,
    112,
    139,
    163,
    187,
    208,
    238,
    240,
    270
   ],
   [
    18,
    46,
    49,
    74,
    113,
    140,
    164,
    188,
    209,
    239,
    241,
    271
   ],
   [
    19,
    47,
    50,
    75,
    114,
    141,
    165,
    189,
    210,
    232,
    242,
    264
   ],
   [
    20,
    40,
    51,
    76,
    115,
    142,
    166,
    190,
    211,
    233,
    243,
    265
   ]
  ],
  "Z": [
   [
    4,
    25,
    49,
    94,
    116,
    126,
    164,
    175,
    195,
    217,
    244,
    283
   ],
   [
    5,
    26,
    50,
    95,
    117,
    127,
    165,
    168,
    196,
    218,
    245,
    284
   ],
   [
    6,
    27,
    51,
    88,
    118,
    120,
    166,
    169,
    197,
    219,
    246,
    285
   ],
   [
    7,
    28,
    52,
    89,
    119,
    121,
    167,
    170,
    198,
    220,
    247,
    286
   ],
   [
    0,
    29,
    53,
    90,
    112,
    122,
    160,
    171,
    199,
    221,
    240,
    287
   ],
   [
    1,
    30,
    54,
    91,
    113,
    123,
    161,
    172,
    192,
    222,
    241,
    280
   ],
   [
    2,
    31,
    55,
    92,
    114,
    124,
    162,
    173,
    193,
    223,
    242,
    281
   ],
   [
    3,
    24,
    48,
    93,
    115,
    125,
    163,
    174,
    194,
    216,
    243,
    282
   ],
   [
    12,
    33,
    57,
    86,
    100,
    134,
    148,
    183,
    203,
    225,
    252,
    275
   ],
   [
    13,
    34,
    58,
    87,
    101,
    135,
    149,
    176,
    204,
    226,
    253,
    276
   ],
   [
    14,
    35,
    59,
    80,
    102,
    128,
    150,
    177,
    205,
    227,
    254,
    277
   ],
   [
    15,
    36,
    60,
    81,
    103,
    129,
    151,
    178,
    206,
    228,
    255,
    278
   ],
   [
    8,
    37,
    61,
    82,
    96,
    130,
    144,
    179,
    207,
    229,
    248,
    279
   ],
   [
    9,
    38,
    62,
    83,
    97,
    131,
    145,
    180,
    200,
    230,
    249,
    272
   ],
   [
    10,
    39,
    63,
    84,
    98,
    132,
    146,
    181,
    201,
    231,
    250,
    273
   ],
   [
    11,
    32,
    56,
    85,
    99,
    133,
    147,
    182,
    202,
    224,
    251,
    274
   ],
   [
    20,
    41,
    65,
    78,
    108,
    142,
    156,
    191,
    211,
    233,
    260,
    267
   ],
   [
    21,
    42,
    66,
    79,
    109,
    143,
    157,
    184,
    212,
    234,
    261,
    268
   ],
   [
    22,
    43,
    67,
    72,
    110,
    136,
    158,
    185,
    213,
    235,
    262,
    269
   ],
   [
    23,
    44,
    68,
    73,
    111,
    137,
    159,
    186,
    214,
    236,
    263,
    270
   ],
   [
    16,
    45,
    69,
    74,
    104,
    138,
    152,
    187,
    215,
    237,
    256,
    271
   ],
   [
    17,
    46,
    70,
    75,
    105,
    139,
    153,
    188,
    208,
    238,
    257,
    264
   ],
   [
    18,
    47,
    71,
    76,
    106,
    140,
    154,
    189,
    209,
    239,
    258,
    265
   ],
   [
    19,
    40,
    64,
    77,
    107,
    141,
    155,
    190,
    210,
    232,
    259,
    266
   ],
   [
    6,
    28,
    49,
    73,
    118,
    140,
    163,
    188,
    199,
    219,
    241,
    268
   ],
   [
    7,
    29,
    50,
    74,
    119,
    141,
    164,
    189,
    192,
    220,
    242,
    269
   ],
   [
    0,
    30,
    51,
    75,
    112,
    142,
    165,
    190,
    193,
    221,
    243,
    270
   ],
   [
    1,
    31,
    52,
    76,
    113,
    143,
    166,
    191,
    194,
    222,
    244,
    271
   ],
   [
    2,
    24,
    53,
    77,
    114,
    136,
    167,
    184,
    195,
    223,
    245,
    264
   ],
   [
    3,
    25,
    54,
    78,
    115,
    137,
    160,
    185,
    196,
    216,
    246,
    265
   ],
   [
    4,
    26,
    55,
    79,
    116,
    138,
    161,
    186,
    197,
    217,
    247,
    266
   ],
   [
    5,
    27,
    48,
    72,
    117,
    139,
    162,
    187,
    198,
    218,
    240,
    267
   ],
   [
    14,
    36,
    57,
    81,
    110,
    124,
    155,
    172,
    207,
    227,
    249,
    276
   ],
   [
    15,
    37,
    58,
    82,
    111,
    125,
    156,
    173,
    200,
    228,
    250,
    277
   ],
   [
    8,
    38,
    59,
    83,
    104,
    126,
    157,
    174,
    201,
    229,
    251,
    278
   ],
   [
    9,
    39,
    60,
    84,
    105,
    127,
    158,
    175,
    202,
    230,
    252,
    279
   ],
   [
    10,
    32,
    61,
    85,
    106,
    120,
    159,
    168,
    203,
    231,
    253,
    272
   ],
   [
    11,
    33,
    62,
    86,
    107,
    121,
    152,
    169,
    204,
    224,
    254,
    273
   ],
   [
    12,
    34,
    63,
    87,
    108,
    122,
    153,
    170,
    205,
    225,
    255,
    274
   ],
   [
    13,
    35,
    56,
    80,
    109,
    123,
    154,
    171,
    206,
    226,
    248,
    275
   ],
   [
    22,
    44,
    65,
    89,
    102,
    132,
    147,
    180,
    215,
    235,
    257,
    284
   ],
   [
    23,
    45,
    66,
    90,
    103,
    133,
    148,
    181,
    208,
    236,
    258,
    285
   ],
   [
    16,
    46,
    67,
    91,
    96,
    134,
    149,
    182,
    209,
    237,
    259,
    286
   ],
   [
    17,
    47,
    68,
    92,
    97,
    135,
    150,
    183,
    210,
    238,
    260,
    287
   ],
   [
    18,
    40,
    69,
    93,
    98,
    128,
    151,
    176,
    211,
    239,
    261,
    280
   ],
   [
    19,
    41,
    70,
    94,
    99,
    129,
    144,
    177,
    212,
    232,
    262,
    281
   ],
   [
    20,
    42,
    71,
    95,
    100,
    130,
    145,
    178,
    213,
    233,
    263,
    282
   ],
   [
    21,
    43,
    64,
    88,
    101,
    131,
    146,
    179,
    214,
    234,
    256,
    283
   ],
   [
    20,
    30,
    52,
    73,
    97,
    142,
    148,
    187,
    212,
    223,
    243,
    265
   ],
   [
    21,
    31,
    53,
    74,
    98,
    143,
    149,
    188,
    213,
    216,
    244,
    266
   ],
   [
    22,
    24,
    54,
    75,
    99,
    136,
    150,
    189,
    214,
    217,
    245,
    267
   ],
   [
    23,
    25,
    55,
    76,
    100,
    137,
    151,
    190,
    215,
    218,
    246,
    268
   ],
   [
    16,
    26,
    48,
    77,
    101,
    138,
    144,
    191,
    208,
    219,
    247,
    269
   ],
   [
    17,
    27,
    49,
    78,
    102,
    139,
    145,
    184,
    209,
    220,
    240,
    270
   ],
   [
    18,
    28,
    50,
    79,
    103,
    140,
    146,
    185,
    210,
    221,
    241,
    271
   ],
   [
    19,
    29,
    51,
    72,
    96,
    141,
    147,
    186,
    211,
    222,
    242,
    264
   ],
   [
    4,
    38,
    60,
    81,
    105,
    134,
    156,
    179,
    196,
    231,
    251,
    273
   ],
   [
    5,
    39,
    61,
    82,
    106,
    135,
    157,
    180,
    197,
    224,
    252,
    274
   ],
   [
    6,
    32,
    62,
    83,
    107,
    128,
    158,
    181,
    198,
    225,
    253,
    275
   ],
   [
    7,
    33,
    63,
    84,
    108,
    129,
    159,
    182,
    199,
    226,
    254,
    276
   ],
   [
    0,
    34,
    56,
    85,
    109,
    130,
    152,
    183,
    192,
    227,
    255,
    277
   ],
   [
    1,
    35,
    57,
    86,
    110,
    131,
    153,
    176,
    193,
    228,
    248,
    278
   ],
   [
    2,
    36,
    58,
    87,
    111,
    132,
    154,
    177,
    194,
    229,
    249,
    279
   ],
   [
    3,
    37,
    59,
    80,
    104,
    133,
    155,
    178,
    195,
    230,
    250,
    272
   ],
   [
    12,
    46,
    68,
    89,
    113,
    126,
    164,
    171,
    204,
    239,
    259,
    281
   ],
   [
    13,
    47,
    69,
    90,
    114,
    127,
    165,
    172,
    205,
    232,
    260,
    282
   ],
   [
    14,
    40,
    70,
    91,
    115,
    120,
    166,
    173,
    206,
    233,
    261,
    283
   ],
   [
    15,
    41,
    71,
    92,
    116,
    121,
    167,
    174,
    207,
    234,
    262,
    284
   ],
   [
    8,
    42,
    64,
    93,
    117,
    122,
    160,
    175,
    200,
    235,
    263,
    285
   ],
   [
    9,
    43,
    65,
    94,
    118,
    123,
    161,
    168,
    201,
    236,
    256,
    286
   ],
   [
    10,
    44,
    66,
    95,
    119,
    124,
    162,
    169,
    202,
    237,
    257,
    287
   ],
   [
    11,
    45,
    67,
    88,
    112,
    125,
    163,
    170,
    203,
    238,
    258,
    280
   ]
  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    67,
    91,
    115,
    163,
    185,
    241
   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    35,
    80,
    109,
    129,
    227,
    277
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Cornucopia code (Lu, Li & Deng, arXiv:2608.02773; block-convolutional CSS construction with the check matrices given in the Methods of arXiv:2610.19073): q=8, n=36q=288 data qubits in twelve 3x8 tiles L0..L5,R0..R5 plus nine 3x8 X-check and nine 3x8 Z-check tiles; HX=[A_(j-i)|B_(j-i)], HZ=[B^-1_(i-j)|A^-1_(i-j)] with the coordinate permutations A_p,B_p:(r,c)|->(rho(p,r),c+s[p]) on Z_3 x Z_8, row maps rho_A(0)=r+1, rho_A(1)=2r+2, rho_B(2)=r+1, rho_B(3)=2r+2 (identity otherwise), and column shifts sA=[4, 5, 4, 7, 5, 1], sB=[4, 2, 4, 2, 7, 7]. These shifts were found by a random shift search; the paper publishes instances only at q=7,16,25,29,49,64,79. Weight-12 checks, k=18q+4=148.",
  "origin": "submission",
  "date": "2026-10-15",
  "model": "MiMo-V2.6-Flash",
  "search_budget": {
   "candidates_screened": 1200,
   "ris_trials_per_side": 100000,
   "tool": "OpenCode agent, MiMo-V2.6-Flash",
   "notes": "uniform random shift search, 3-stage RIS ladder (100/4000/100000 trials), see research note"
  },
  "references": [
   "arXiv:2608.02773",
   "arXiv:2610.19073"
  ]
 },
 "family": "other"
}
