[[201,78,3]] · QEC Challenge

[[201,78,3]] d =

201

kd²/n

3.493

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)

[19, 21, 22]

d_Z 3 · witness weight 3 (claimed upper_bound)

witness operator (support, 3 qubits)

[7, 115, 127]

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 17.833) · H_Z 4–9 (mean 6.247)

qubit degrees H_X 1–5 (mean 2.662) · H_Z 1–16 (mean 2.891)

trapping sets H_X (1,1)×30 (2,1)×450 (3,0)×930 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 30 (1,2): 60 (1,3): 65 (1,4): 40 (1,5): 6 (2,1): 450 (2,2): 855 (2,3): 830 (2,4): 495 (2,5): 300 (2,6): 175 (2,7): 40 (3,0): 930 (3,1): 4215 (3,2): 7995 (3,3): 9205 (3,4): 9690 (3,5): 10960 (3,6): 9440 (3,7): 5970 (3,8): 2620 (3,9): 625 (3,10): 60

trapping sets H_Z (1,1)×62 (2,1)×217 (3,0)×124 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,1): 62 (1,2): 93 (1,3): 31 (1,16): 15 (2,1): 217 (2,2): 155 (2,15): 160 (2,16): 510 (2,17): 240 (3,0): 124 (3,1): 248 (3,2): 124 (3,3): 62 (3,14): 1200 (3,15): 5680 (3,16): 11390 (3,17): 8640 (3,18): 2680 (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 sham6

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 30 (max weight 19) · Z-checks 93 (max weight 9)

H_X (30 checks, sparse supports)

[0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 187] [1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 145, 157, 169, 181, 186, 187] [2, 14, 26, 38, 50, 62, 74, 86, 98, 110, 122, 134, 146, 158, 170, 182, 188] [3, 15, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 147, 159, 171, 183, 186, 188] [4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 148, 160, 172, 184, 187, 188] [5, 17, 29, 41, 53, 65, 77, 89, 101, 113, 125, 137, 149, 161, 173, 185, 186, 187, 188] [6, 12, 30, 36, 54, 60, 78, 84, 102, 108, 126, 132, 150, 156, 174, 180, 190] [7, 13, 31, 37, 55, 61, 79, 85, 103, 109, 127, 133, 151, 157, 175, 181, 189, 190] [8, 14, 32, 38, 56, 62, 80, 86, 104, 110, 128, 134, 152, 158, 176, 182, 191] [9, 15, 33, 39, 57, 63, 81, 87, 105, 111, 129, 135, 153, 159, 177, 183, 189, 191] [10, 16, 34, 40, 58, 64, 82, 88, 106, 112, 130, 136, 154, 160, 178, 184, 190, 191] [11, 17, 35, 41, 59, 65, 83, 89, 107, 113, 131, 137, 155, 161, 179, 185, 189, 190, 191] [18, 24, 30, 36, 66, 72, 78, 84, 114, 120, 126, 132, 162, 168, 174, 180, 193] [19, 25, 31, 37, 67, 73, 79, 85, 115, 121, 127, 133, 163, 169, 175, 181, 192, 193] [20, 26, 32, 38, 68, 74, 80, 86, 116, 122, 128, 134, 164, 170, 176, 182, 194] [21, 27, 33, 39, 69, 75, 81, 87, 117, 123, 129, 135, 165, 171, 177, 183, 192, 194] [22, 28, 34, 40, 70, 76, 82, 88, 118, 124, 130, 136, 166, 172, 178, 184, 193, 194] [23, 29, 35, 41, 71, 77, 83, 89, 119, 125, 131, 137, 167, 173, 179, 185, 192, 193, 194] [42, 48, 54, 60, 66, 72, 78, 84, 138, 144, 150, 156, 162, 168, 174, 180, 196] [43, 49, 55, 61, 67, 73, 79, 85, 139, 145, 151, 157, 163, 169, 175, 181, 195, 196] [44, 50, 56, 62, 68, 74, 80, 86, 140, 146, 152, 158, 164, 170, 176, 182, 197] [45, 51, 57, 63, 69, 75, 81, 87, 141, 147, 153, 159, 165, 171, 177, 183, 195, 197] [46, 52, 58, 64, 70, 76, 82, 88, 142, 148, 154, 160, 166, 172, 178, 184, 196, 197] [47, 53, 59, 65, 71, 77, 83, 89, 143, 149, 155, 161, 167, 173, 179, 185, 195, 196, 197] [90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 199] [91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 181, 198, 199] [92, 98, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 182, 200] [93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 198, 200] [94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 199, 200] [95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 198, 199, 200]

H_Z (93 checks, sparse supports)

[1, 3, 5, 186] [0, 1, 4, 5, 187] [2, 3, 4, 5, 188] [7, 9, 11, 189] [6, 7, 10, 11, 190] [8, 9, 10, 11, 191] [13, 15, 17, 186, 189] [12, 13, 16, 17, 187, 190] [14, 15, 16, 17, 188, 191] [19, 21, 23, 192] [18, 19, 22, 23, 193] [20, 21, 22, 23, 194] [25, 27, 29, 186, 192] [24, 25, 28, 29, 187, 193] [26, 27, 28, 29, 188, 194] [31, 33, 35, 189, 192] [30, 31, 34, 35, 190, 193] [32, 33, 34, 35, 191, 194] [37, 39, 41, 186, 189, 192] [36, 37, 40, 41, 187, 190, 193] [38, 39, 40, 41, 188, 191, 194] [43, 45, 47, 195] [42, 43, 46, 47, 196] [44, 45, 46, 47, 197] [49, 51, 53, 186, 195] [48, 49, 52, 53, 187, 196] [50, 51, 52, 53, 188, 197] [55, 57, 59, 189, 195] [54, 55, 58, 59, 190, 196] [56, 57, 58, 59, 191, 197] [61, 63, 65, 186, 189, 195] [60, 61, 64, 65, 187, 190, 196] [62, 63, 64, 65, 188, 191, 197] [67, 69, 71, 192, 195] [66, 67, 70, 71, 193, 196] [68, 69, 70, 71, 194, 197] [73, 75, 77, 186, 192, 195] [72, 73, 76, 77, 187, 193, 196] [74, 75, 76, 77, 188, 194, 197] [79, 81, 83, 189, 192, 195] [78, 79, 82, 83, 190, 193, 196] [80, 81, 82, 83, 191, 194, 197] [85, 87, 89, 186, 189, 192, 195] [84, 85, 88, 89, 187, 190, 193, 196] [86, 87, 88, 89, 188, 191, 194, 197] [91, 93, 95, 198] [90, 91, 94, 95, 199] [92, 93, 94, 95, 200] [97, 99, 101, 186, 198] [96, 97, 100, 101, 187, 199] [98, 99, 100, 101, 188, 200] [103, 105, 107, 189, 198] [102, 103, 106, 107, 190, 199] [104, 105, 106, 107, 191, 200] [109, 111, 113, 186, 189, 198] [108, 109, 112, 113, 187, 190, 199] [110, 111, 112, 113, 188, 191, 200] [115, 117, 119, 192, 198] [114, 115, 118, 119, 193, 199] [116, 117, 118, 119, 194, 200] [121, 123, 125, 186, 192, 198] [120, 121, 124, 125, 187, 193, 199] [122, 123, 124, 125, 188, 194, 200] [127, 129, 131, 189, 192, 198] [126, 127, 130, 131, 190, 193, 199] [128, 129, 130, 131, 191, 194, 200] [133, 135, 137, 186, 189, 192, 198] [132, 133, 136, 137, 187, 190, 193, 199] [134, 135, 136, 137, 188, 191, 194, 200] [139, 141, 143, 195, 198] [138, 139, 142, 143, 196, 199] [140, 141, 142, 143, 197, 200] [145, 147, 149, 186, 195, 198] [144, 145, 148, 149, 187, 196, 199] [146, 147, 148, 149, 188, 197, 200] [151, 153, 155, 189, 195, 198] [150, 151, 154, 155, 190, 196, 199] [152, 153, 154, 155, 191, 197, 200] [157, 159, 161, 186, 189, 195, 198] [156, 157, 160, 161, 187, 190, 196, 199] [158, 159, 160, 161, 188, 191, 197, 200] [163, 165, 167, 192, 195, 198] [162, 163, 166, 167, 193, 196, 199] [164, 165, 166, 167, 194, 197, 200] [169, 171, 173, 186, 192, 195, 198] [168, 169, 172, 173, 187, 193, 196, 199] [170, 171, 172, 173, 188, 194, 197, 200] [175, 177, 179, 189, 192, 195, 198] [174, 175, 178, 179, 190, 193, 196, 199] [176, 177, 178, 179, 191, 194, 197, 200] [181, 183, 185, 186, 189, 192, 195, 198] [180, 181, 184, 185, 187, 190, 193, 196, 199] [182, 183, 184, 185, 188, 191, 194, 197, 200]

Code ID 201-78-3 · download JSON · raw on GitHub