[[152,42,8]] · QEC Challenge

[[152,42,8]] d =

152

kd²/n

17.684

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 8, d_Z = 8 · w_X = 8, 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 8 · witness weight 8 (claimed upper_bound)

witness operator (support, 8 qubits)

[7, 38, 49, 60, 103, 106, 110, 141]

d_Z 8 · witness weight 8 (claimed upper_bound)

witness operator (support, 8 qubits)

[28, 29, 32, 37, 50, 54, 117, 119]

certificate exact, d = 8 · CryptoMiniSat 5.14.7 SAT

X: no logical < 8 exists; Z: no logical < 8 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 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 8 · H_Z 8

qubit degrees H_X 3 · H_Z 3

trapping sets H_X (1,3)×152 (2,4)×1596 (3,3)×228 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,3): 152 (2,4): 1596 (3,3): 228 (3,5): 21660 (3,7): 3192

trapping sets H_Z (1,3)×152 (2,4)×1596 (3,3)×228 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,3): 152 (2,4): 1596 (3,3): 228 (3,5): 21660 (3,7): 3192

Construction & provenance

authors Lee, Jong Yeon

provenance literature baseline

construction Cyclic all-one pair-partition CPM CSS construction (arXiv:2607.14091), instance PPS152_n152_k42_d8 (internal id j3l8_p19_00016): lift size p=19, (J,L)=(3,8), n=8*p=152, 3*p=57 checks per side, column weight 3, row weight 8. CPM exponent arrays (rows = CPM block-rows, columns = the 8 block-columns): E_X = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 10, 9, 3, 7, 1, 18, 15], [0, 12, 17, 14, 8, 16, 13, 6]], E_Z = [[0, 15, 8, 4, 8, 0, 4, 15], [0, 1, 2, 6, 0, 1, 2, 6], [0, 6, 16, 7, 7, 16, 6, 0]]. Lift convention per the authors' expand_and_verify_cpm_matrices.py (github.com/kasaikenta/pair-partition-cpm-css-codes @ 9c2a6f2): check a of block-row b on side S has support {8*((a - E_S[b][t]) mod 19) + t : t=0..7}. Source file https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/contributed_codes/jong_yeon_lee/codes/PPS152_n152_k42_d8.cpm (sha256 2c0b11059910a4353a746713100720db0e73214abcdd204973206d5af954a897), expanded with the authors' own script.

model classical construction (no AI model)

reference arXiv:2607.14091

date 2026

notes Literature baseline, seeded 2026-08-14. Listed as PPS152 [[152,42,8]] in the contributed-codes section (Jong Yeon Lee, 19 CPM-PP codes) of the Okada-Kasai pair-partition CPM catalogue (arXiv:2607.14091; catalogue page updated 2026-08-13), which reports the distance as exact. No public machine-verified distance certificate bundle covers this instance (checked master_manifest.json of certificate_bundles_20260805), so it is recorded here strictly as a witness-backed upper bound from this repo's own 200000-trial RIS search per side (seed 11). Reproduction was validated end to end: the published .cpm file expanded with the authors' own script gives a CSS-orthogonal regular pair with the claimed k.

family pair-partition CPM (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 57 (max weight 8) · Z-checks 57 (max weight 8)

H_X (57 checks, sparse supports)

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

H_Z (57 checks, sparse supports)

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

Code ID 152-42-8 · download JSON · raw on GitHub