[[117,44,3]] · QEC Challenge

[[117,44,3]] d =

117

kd²/n

3.385

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 3, d_Z = 3 · w_X = 11, w_Z = 8 (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)

[77, 78, 79]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[43, 64, 85]

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 9–11 (mean 9.714) · H_Z 5–8 (mean 6.133)

qubit degrees H_X 1–4 (mean 2.325) · H_Z 1–8 (mean 2.359)

trapping sets H_X (1,1)×28 (2,1)×196 (3,0)×245 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 28 (1,2): 42 (1,3): 28 (1,4): 19 (2,1): 196 (2,2): 252 (2,3): 160 (2,4): 156 (2,5): 144 (2,6): 48 (3,0): 245 (3,1): 784 (3,2): 996 (3,3): 1320 (3,4): 2246 (3,5): 2760 (3,6): 1920 (3,7): 984 (3,8): 240

trapping sets H_Z (1,1)×45 (2,1)×135 (3,0)×105 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 45 (1,2): 45 (1,3): 15 (1,8): 12 (2,1): 135 (2,2): 90 (2,7): 96 (2,8): 210 (2,9): 96 (3,0): 105 (3,1): 180 (3,2): 90 (3,3): 45 (3,6): 336 (3,7): 1776 (3,8): 2700 (3,9): 1944 (3,10): 672 (3,11): 72 (3,14): 240 (3,15): 240

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction Hypergraph product of classical codes ham15 and ham7

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 28 (max weight 11) · Z-checks 45 (max weight 8)

H_X (28 checks, sparse supports)

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

H_Z (45 checks, sparse supports)

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

Code ID 117-44-3 · download JSON · raw on GitHub