[[104,30,8]] · QEC Challenge

[[104,30,8]] d =

104

kd²/n

18.462

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)

[0, 17, 55, 65, 75, 84, 94, 99]

d_Z 8 · witness weight 8 (claimed upper_bound)

witness operator (support, 8 qubits)

[21, 23, 80, 83, 93, 95, 102, 103]

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)×104 (2,4)×1092 (3,3)×364 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,3): 104 (2,4): 1092 (3,3): 364 (3,5): 14196 (3,7): 2184

trapping sets H_Z (1,3)×104 (2,4)×1092 (3,3)×364 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,3): 104 (2,4): 1092 (3,3): 364 (3,5): 14196 (3,7): 2184

Construction & provenance

authors Lee, Jong Yeon

provenance literature baseline

construction Cyclic all-one pair-partition CPM CSS construction (arXiv:2607.14091), instance PPS104_n104_k30_d8 (internal id j3l8_p13_00382): lift size p=13, (J,L)=(3,8), n=8*p=104, 3*p=39 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, 7, 11, 5, 2, 12, 6, 3], [0, 2, 7, 9, 1, 5, 4, 8]], E_Z = [[0, 4, 12, 3, 3, 12, 4, 0], [0, 1, 3, 4, 1, 4, 0, 3], [0, 5, 6, 11, 0, 5, 6, 11]]. 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 13) + 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/PPS104_n104_k30_d8.cpm (sha256 f40ebdb9f2a12e39ccecd49c5b7e537ef0b989cbb19a8cab8e4782b31a640753), 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 PPS104 [[104,30,8]] 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 39 (max weight 8) · Z-checks 39 (max weight 8)

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

H_Z (39 checks, sparse supports)

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

Code ID 104-30-8 · download JSON · raw on GitHub