[[170,52,3]] · QEC Challenge

[[170,52,3]] d =

170

kd²/n

2.753

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 19, w_Z = 9 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[45, 46, 49]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[33, 78, 113]

certificate exact, d = 3 · scipy/HiGHS MILP

X: no logical < 3 exists; Z: no logical < 3 exists

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 17–19 (mean 18.0) · H_Z 4–9 (mean 5.914)

qubit degrees H_X 1–5 (mean 2.647) · H_Z 1–16 (mean 3.235)

trapping sets H_X (1,1)×25 (2,1)×375 (3,0)×775 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,1): 25 (1,2): 50 (1,3): 60 (1,4): 30 (1,5): 5 (2,1): 375 (2,2): 735 (2,3): 750 (2,4): 460 (2,5): 240 (2,6): 110 (2,7): 20 (3,0): 775 (3,1): 3540 (3,2): 7095 (3,3): 8850 (3,4): 9690 (3,5): 9485 (3,6): 7110 (3,7): 3950 (3,8): 1460 (3,9): 310 (3,10): 30

trapping sets H_Z (1,1)×31 (2,1)×155 (3,0)×62 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,1): 31 (1,2): 93 (1,3): 31 (1,16): 15 (2,1): 155 (2,2): 124 (2,15): 80 (2,16): 510 (2,17): 240 (3,0): 62 (3,1): 155 (3,2): 62 (3,3): 31 (3,14): 600 (3,15): 2960 (3,16): 10030 (3,17): 8400 (3,18): 2600 (3,19): 240 (3,30): 720 (3,31): 720

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction Hypergraph product of classical codes ham31 and sham5

model Tencent Hy3 (claimed, not verified)

builds on arXiv:0903.0566

date 2026-07-17

family hypergraph product (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (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 25 (max weight 19) · Z-checks 93 (max weight 9)

H_X (25 checks, sparse supports)

[0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 155, 156] [1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 121, 131, 141, 151, 157] [2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 152, 155, 157] [3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, 123, 133, 143, 153, 156, 157] [4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144, 154, 155, 156, 157] [5, 10, 25, 30, 45, 50, 65, 70, 85, 90, 105, 110, 125, 130, 145, 150, 158, 159] [6, 11, 26, 31, 46, 51, 66, 71, 86, 91, 106, 111, 126, 131, 146, 151, 160] [7, 12, 27, 32, 47, 52, 67, 72, 87, 92, 107, 112, 127, 132, 147, 152, 158, 160] [8, 13, 28, 33, 48, 53, 68, 73, 88, 93, 108, 113, 128, 133, 148, 153, 159, 160] [9, 14, 29, 34, 49, 54, 69, 74, 89, 94, 109, 114, 129, 134, 149, 154, 158, 159, 160] [15, 20, 25, 30, 55, 60, 65, 70, 95, 100, 105, 110, 135, 140, 145, 150, 161, 162] [16, 21, 26, 31, 56, 61, 66, 71, 96, 101, 106, 111, 136, 141, 146, 151, 163] [17, 22, 27, 32, 57, 62, 67, 72, 97, 102, 107, 112, 137, 142, 147, 152, 161, 163] [18, 23, 28, 33, 58, 63, 68, 73, 98, 103, 108, 113, 138, 143, 148, 153, 162, 163] [19, 24, 29, 34, 59, 64, 69, 74, 99, 104, 109, 114, 139, 144, 149, 154, 161, 162, 163] [35, 40, 45, 50, 55, 60, 65, 70, 115, 120, 125, 130, 135, 140, 145, 150, 164, 165] [36, 41, 46, 51, 56, 61, 66, 71, 116, 121, 126, 131, 136, 141, 146, 151, 166] [37, 42, 47, 52, 57, 62, 67, 72, 117, 122, 127, 132, 137, 142, 147, 152, 164, 166] [38, 43, 48, 53, 58, 63, 68, 73, 118, 123, 128, 133, 138, 143, 148, 153, 165, 166] [39, 44, 49, 54, 59, 64, 69, 74, 119, 124, 129, 134, 139, 144, 149, 154, 164, 165, 166] [75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 167, 168] [76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 169] [77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 167, 169] [78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 168, 169] [79, 84, 89, 94, 99, 104, 109, 114, 119, 124, 129, 134, 139, 144, 149, 154, 167, 168, 169]

H_Z (93 checks, sparse supports)

[0, 2, 4, 155] [0, 3, 4, 156] [1, 2, 3, 4, 157] [5, 7, 9, 158] [5, 8, 9, 159] [6, 7, 8, 9, 160] [10, 12, 14, 155, 158] [10, 13, 14, 156, 159] [11, 12, 13, 14, 157, 160] [15, 17, 19, 161] [15, 18, 19, 162] [16, 17, 18, 19, 163] [20, 22, 24, 155, 161] [20, 23, 24, 156, 162] [21, 22, 23, 24, 157, 163] [25, 27, 29, 158, 161] [25, 28, 29, 159, 162] [26, 27, 28, 29, 160, 163] [30, 32, 34, 155, 158, 161] [30, 33, 34, 156, 159, 162] [31, 32, 33, 34, 157, 160, 163] [35, 37, 39, 164] [35, 38, 39, 165] [36, 37, 38, 39, 166] [40, 42, 44, 155, 164] [40, 43, 44, 156, 165] [41, 42, 43, 44, 157, 166] [45, 47, 49, 158, 164] [45, 48, 49, 159, 165] [46, 47, 48, 49, 160, 166] [50, 52, 54, 155, 158, 164] [50, 53, 54, 156, 159, 165] [51, 52, 53, 54, 157, 160, 166] [55, 57, 59, 161, 164] [55, 58, 59, 162, 165] [56, 57, 58, 59, 163, 166] [60, 62, 64, 155, 161, 164] [60, 63, 64, 156, 162, 165] [61, 62, 63, 64, 157, 163, 166] [65, 67, 69, 158, 161, 164] [65, 68, 69, 159, 162, 165] [66, 67, 68, 69, 160, 163, 166] [70, 72, 74, 155, 158, 161, 164] [70, 73, 74, 156, 159, 162, 165] [71, 72, 73, 74, 157, 160, 163, 166] [75, 77, 79, 167] [75, 78, 79, 168] [76, 77, 78, 79, 169] [80, 82, 84, 155, 167] [80, 83, 84, 156, 168] [81, 82, 83, 84, 157, 169] [85, 87, 89, 158, 167] [85, 88, 89, 159, 168] [86, 87, 88, 89, 160, 169] [90, 92, 94, 155, 158, 167] [90, 93, 94, 156, 159, 168] [91, 92, 93, 94, 157, 160, 169] [95, 97, 99, 161, 167] [95, 98, 99, 162, 168] [96, 97, 98, 99, 163, 169] [100, 102, 104, 155, 161, 167] [100, 103, 104, 156, 162, 168] [101, 102, 103, 104, 157, 163, 169] [105, 107, 109, 158, 161, 167] [105, 108, 109, 159, 162, 168] [106, 107, 108, 109, 160, 163, 169] [110, 112, 114, 155, 158, 161, 167] [110, 113, 114, 156, 159, 162, 168] [111, 112, 113, 114, 157, 160, 163, 169] [115, 117, 119, 164, 167] [115, 118, 119, 165, 168] [116, 117, 118, 119, 166, 169] [120, 122, 124, 155, 164, 167] [120, 123, 124, 156, 165, 168] [121, 122, 123, 124, 157, 166, 169] [125, 127, 129, 158, 164, 167] [125, 128, 129, 159, 165, 168] [126, 127, 128, 129, 160, 166, 169] [130, 132, 134, 155, 158, 164, 167] [130, 133, 134, 156, 159, 165, 168] [131, 132, 133, 134, 157, 160, 166, 169] [135, 137, 139, 161, 164, 167] [135, 138, 139, 162, 165, 168] [136, 137, 138, 139, 163, 166, 169] [140, 142, 144, 155, 161, 164, 167] [140, 143, 144, 156, 162, 165, 168] [141, 142, 143, 144, 157, 163, 166, 169] [145, 147, 149, 158, 161, 164, 167] [145, 148, 149, 159, 162, 165, 168] [146, 147, 148, 149, 160, 163, 166, 169] [150, 152, 154, 155, 158, 161, 164, 167] [150, 153, 154, 156, 159, 162, 165, 168] [151, 152, 153, 154, 157, 160, 163, 166, 169]

Code ID 170-52-3 · download JSON · raw on GitHub