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[[128,8,6]] d =
n
128
k
8
d
6
kd²/n
2.25
w
6
g
0.0352
r
2.8284
layers
2

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Distance

d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[16, 33, 34, 50, 52, 64]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[30, 44, 46, 52, 58, 120]
certificate exact, d = 6 · scipy/HiGHS cutoff IP
X: no logical < 6 exists; Z: no logical < 6 exists

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 2.828
X checkZ checkqubit site (64)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release

Construction & provenance

authors Liang, Zijian and Eberhardt, Jens Niklas and Chen, Yu-An
provenance literature baseline
construction Liang-Eberhardt-Chen [[288,8,12]] family, (8,8) lattice.
model classical construction (no AI model)
reference arXiv:2504.08887
date 2025-04-11
notes Reference baseline (Liang, Eberhardt, Chen).
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 60 · Z-checks 60
H_X (60 checks, sparse supports)
[0, 65, 66] [1, 66, 67] [2, 67, 68] [3, 68, 69] [4, 69, 70] [5, 70, 71] [0, 8, 73, 74] [1, 9, 74, 75] [2, 10, 75, 76] [3, 11, 76, 77] [4, 12, 77, 78] [5, 13, 78, 79] [2, 8, 16, 64, 81, 82] [3, 9, 17, 65, 82, 83] [4, 10, 18, 66, 83, 84] [5, 11, 19, 67, 84, 85] [6, 12, 20, 68, 85, 86] [7, 13, 21, 69, 86, 87] [10, 16, 24, 72, 89, 90] [11, 17, 25, 73, 90, 91] [12, 18, 26, 74, 91, 92] [13, 19, 27, 75, 92, 93] [14, 20, 28, 76, 93, 94] [15, 21, 29, 77, 94, 95] [18, 24, 32, 80, 97, 98] [19, 25, 33, 81, 98, 99] [20, 26, 34, 82, 99, 100] [21, 27, 35, 83, 100, 101] [22, 28, 36, 84, 101, 102] [23, 29, 37, 85, 102, 103] [26, 32, 40, 88, 105, 106] [27, 33, 41, 89, 106, 107] [28, 34, 42, 90, 107, 108] [29, 35, 43, 91, 108, 109] [30, 36, 44, 92, 109, 110] [31, 37, 45, 93, 110, 111] [34, 40, 48, 96, 113, 114] [35, 41, 49, 97, 114, 115] [36, 42, 50, 98, 115, 116] [37, 43, 51, 99, 116, 117] [38, 44, 52, 100, 117, 118] [39, 45, 53, 101, 118, 119] [42, 48, 56, 104, 121, 122] [43, 49, 57, 105, 122, 123] [44, 50, 58, 106, 123, 124] [45, 51, 59, 107, 124, 125] [46, 52, 60, 108, 125, 126] [47, 53, 61, 109, 126, 127] [50, 56, 112] [51, 57, 113] [52, 58, 114] [53, 59, 115] [54, 60, 116] [55, 61, 117] [58, 120] [59, 121] [60, 122] [61, 123] [62, 124] [63, 125]
H_Z (60 checks, sparse supports)
[16, 64, 72] [0, 17, 65, 73] [0, 1, 18, 66, 74, 80] [1, 2, 19, 67, 75, 81] [2, 3, 20, 68, 76, 82] [3, 4, 21, 69, 77, 83] [4, 5, 22, 70, 78, 84] [5, 6, 23, 71, 79, 85] [6, 7, 86] [7, 87] [24, 72, 80] [8, 25, 73, 81] [8, 9, 26, 74, 82, 88] [9, 10, 27, 75, 83, 89] [10, 11, 28, 76, 84, 90] [11, 12, 29, 77, 85, 91] [12, 13, 30, 78, 86, 92] [13, 14, 31, 79, 87, 93] [14, 15, 94] [15, 95] [32, 80, 88] [16, 33, 81, 89] [16, 17, 34, 82, 90, 96] [17, 18, 35, 83, 91, 97] [18, 19, 36, 84, 92, 98] [19, 20, 37, 85, 93, 99] [20, 21, 38, 86, 94, 100] [21, 22, 39, 87, 95, 101] [22, 23, 102] [23, 103] [40, 88, 96] [24, 41, 89, 97] [24, 25, 42, 90, 98, 104] [25, 26, 43, 91, 99, 105] [26, 27, 44, 92, 100, 106] [27, 28, 45, 93, 101, 107] [28, 29, 46, 94, 102, 108] [29, 30, 47, 95, 103, 109] [30, 31, 110] [31, 111] [48, 96, 104] [32, 49, 97, 105] [32, 33, 50, 98, 106, 112] [33, 34, 51, 99, 107, 113] [34, 35, 52, 100, 108, 114] [35, 36, 53, 101, 109, 115] [36, 37, 54, 102, 110, 116] [37, 38, 55, 103, 111, 117] [38, 39, 118] [39, 119] [56, 104, 112] [40, 57, 105, 113] [40, 41, 58, 106, 114, 120] [41, 42, 59, 107, 115, 121] [42, 43, 60, 108, 116, 122] [43, 44, 61, 109, 117, 123] [44, 45, 62, 110, 118, 124] [45, 46, 63, 111, 119, 125] [46, 47, 126] [47, 127]
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