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[[170,8,20]] d ≤
n
170
k
8
d
20
kd²/n
18.824
w
10
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 20, d_Z ≤ 20 · w_X = 10, w_Z = 10 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[17, 27, 39, 48, 53, 65, 71, 76, 94, 98, 100, 106, 108, 112, 120, 129, 137, 144, 157, 160]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[14, 17, 44, 49, 56, 59, 63, 65, 71, 78, 92, 95, 107, 109, 110, 112, 122, 128, 143, 148]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

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 10 · H_Z 10
qubit degrees H_X 5 · H_Z 5
trapping sets H_X (1,5)×170 (2,8)×3825 (3,9)×7905 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,5): 170 (2,8): 3825 (3,9): 7905 (3,11): 113985 (3,13): 10200
trapping sets H_Z (1,5)×170 (2,8)×3825 (3,9)×7905 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,5): 170 (2,8): 3825 (3,9): 7905 (3,11): 113985 (3,13): 10200

Construction & provenance

authors Lee, Jong Yeon
provenance literature baseline
construction Cyclic all-one pair-partition CPM CSS construction (arXiv:2607.14091), instance PPS170_n170_k8_d20 (internal id j5l10_p17_c0000): lift size p=17, (J,L)=(5,10), n=10*p=170, 5*p=85 checks per side, column weight 5, row weight 10. CPM exponent arrays (rows = CPM block-rows, columns = the 10 block-columns): E_X = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 15, 4, 3, 8, 7, 6, 5, 10, 2], [0, 16, 12, 5, 3, 1, 10, 14, 13, 15], [0, 10, 11, 12, 4, 9, 3, 16, 8, 1], [0, 6, 10, 16, 15, 11, 1, 2, 9, 7]], E_Z = [[0, 11, 8, 15, 6, 11, 6, 0, 8, 15], [0, 7, 9, 14, 10, 9, 0, 14, 10, 7], [0, 1, 16, 13, 2, 0, 1, 16, 13, 2], [0, 9, 3, 1, 5, 1, 3, 5, 9, 0], [0, 2, 1, 10, 7, 7, 10, 2, 0, 1]]. 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 {10*((a - E_S[b][t]) mod 17) + t : t=0..9}. Source file https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/contributed_codes/jong_yeon_lee/codes/PPS170_n170_k8_d20.cpm (sha256 4dbb0cbdfb14734094f05e6eda96b006f9379dcfbdc6200d262c72f09b337f14), 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 PPS170 [[170,8,20]] 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 300000-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 85 (max weight 10) · Z-checks 85 (max weight 10)
H_X (85 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, 152, 153, 154, 155, 156, 157, 158, 159] [160, 161, 162, 163, 164, 165, 166, 167, 168, 169] [0, 21, 78, 94, 105, 116, 127, 132, 143, 159] [10, 31, 88, 104, 115, 126, 137, 142, 153, 169] [9, 20, 41, 98, 114, 125, 136, 147, 152, 163] [3, 19, 30, 51, 108, 124, 135, 146, 157, 162] [2, 13, 29, 40, 61, 118, 134, 145, 156, 167] [7, 12, 23, 39, 50, 71, 128, 144, 155, 166] [6, 17, 22, 33, 49, 60, 81, 138, 154, 165] [5, 16, 27, 32, 43, 59, 70, 91, 148, 164] [4, 15, 26, 37, 42, 53, 69, 80, 101, 158] [14, 25, 36, 47, 52, 63, 79, 90, 111, 168] [8, 24, 35, 46, 57, 62, 73, 89, 100, 121] [18, 34, 45, 56, 67, 72, 83, 99, 110, 131] [28, 44, 55, 66, 77, 82, 93, 109, 120, 141] [38, 54, 65, 76, 87, 92, 103, 119, 130, 151] [48, 64, 75, 86, 97, 102, 113, 129, 140, 161] [1, 58, 74, 85, 96, 107, 112, 123, 139, 150] [11, 68, 84, 95, 106, 117, 122, 133, 149, 160] [0, 11, 29, 37, 48, 52, 76, 123, 144, 165] [5, 10, 21, 39, 47, 58, 62, 86, 133, 154] [15, 20, 31, 49, 57, 68, 72, 96, 143, 164] [4, 25, 30, 41, 59, 67, 78, 82, 106, 153] [14, 35, 40, 51, 69, 77, 88, 92, 116, 163] [3, 24, 45, 50, 61, 79, 87, 98, 102, 126] [13, 34, 55, 60, 71, 89, 97, 108, 112, 136] [23, 44, 65, 70, 81, 99, 107, 118, 122, 146] [33, 54, 75, 80, 91, 109, 117, 128, 132, 156] [43, 64, 85, 90, 101, 119, 127, 138, 142, 166] [6, 53, 74, 95, 100, 111, 129, 137, 148, 152] [16, 63, 84, 105, 110, 121, 139, 147, 158, 162] [2, 26, 73, 94, 115, 120, 131, 149, 157, 168] [8, 12, 36, 83, 104, 125, 130, 141, 159, 167] [7, 18, 22, 46, 93, 114, 135, 140, 151, 169] [9, 17, 28, 32, 56, 103, 124, 145, 150, 161] [1, 19, 27, 38, 42, 66, 113, 134, 155, 160] [0, 17, 53, 62, 71, 85, 98, 134, 146, 169] [9, 10, 27, 63, 72, 81, 95, 108, 144, 156] [19, 20, 37, 73, 82, 91, 105, 118, 154, 166] [6, 29, 30, 47, 83, 92, 101, 115, 128, 164] [4, 16, 39, 40, 57, 93, 102, 111, 125, 138] [14, 26, 49, 50, 67, 103, 112, 121, 135, 148] [24, 36, 59, 60, 77, 113, 122, 131, 145, 158] [34, 46, 69, 70, 87, 123, 132, 141, 155, 168] [8, 44, 56, 79, 80, 97, 133, 142, 151, 165] [5, 18, 54, 66, 89, 90, 107, 143, 152, 161] [1, 15, 28, 64, 76, 99, 100, 117, 153, 162] [2, 11, 25, 38, 74, 86, 109, 110, 127, 163] [3, 12, 21, 35, 48, 84, 96, 119, 120, 137] [13, 22, 31, 45, 58, 94, 106, 129, 130, 147] [23, 32, 41, 55, 68, 104, 116, 139, 140, 157] [33, 42, 51, 65, 78, 114, 126, 149, 150, 167] [7, 43, 52, 61, 75, 88, 124, 136, 159, 160] [0, 13, 24, 65, 72, 88, 109, 111, 157, 166] [6, 10, 23, 34, 75, 82, 98, 119, 121, 167] [7, 16, 20, 33, 44, 85, 92, 108, 129, 131] [17, 26, 30, 43, 54, 95, 102, 118, 139, 141] [27, 36, 40, 53, 64, 105, 112, 128, 149, 151] [37, 46, 50, 63, 74, 115, 122, 138, 159, 161] [1, 47, 56, 60, 73, 84, 125, 132, 148, 169] [9, 11, 57, 66, 70, 83, 94, 135, 142, 158] [19, 21, 67, 76, 80, 93, 104, 145, 152, 168] [8, 29, 31, 77, 86, 90, 103, 114, 155, 162] [2, 18, 39, 41, 87, 96, 100, 113, 124, 165] [5, 12, 28, 49, 51, 97, 106, 110, 123, 134] [15, 22, 38, 59, 61, 107, 116, 120, 133, 144] [25, 32, 48, 69, 71, 117, 126, 130, 143, 154] [35, 42, 58, 79, 81, 127, 136, 140, 153, 164] [4, 45, 52, 68, 89, 91, 137, 146, 150, 163] [3, 14, 55, 62, 78, 99, 101, 147, 156, 160]
H_Z (85 checks, sparse supports)
[0, 7, 23, 29, 61, 65, 92, 98, 114, 116] [10, 17, 33, 39, 71, 75, 102, 108, 124, 126] [20, 27, 43, 49, 81, 85, 112, 118, 134, 136] [30, 37, 53, 59, 91, 95, 122, 128, 144, 146] [40, 47, 63, 69, 101, 105, 132, 138, 154, 156] [50, 57, 73, 79, 111, 115, 142, 148, 164, 166] [4, 6, 60, 67, 83, 89, 121, 125, 152, 158] [14, 16, 70, 77, 93, 99, 131, 135, 162, 168] [2, 8, 24, 26, 80, 87, 103, 109, 141, 145] [12, 18, 34, 36, 90, 97, 113, 119, 151, 155] [22, 28, 44, 46, 100, 107, 123, 129, 161, 165] [1, 5, 32, 38, 54, 56, 110, 117, 133, 139] [11, 15, 42, 48, 64, 66, 120, 127, 143, 149] [21, 25, 52, 58, 74, 76, 130, 137, 153, 159] [31, 35, 62, 68, 84, 86, 140, 147, 163, 169] [3, 9, 41, 45, 72, 78, 94, 96, 150, 157] [13, 19, 51, 55, 82, 88, 104, 106, 160, 167] [0, 6, 33, 37, 74, 78, 82, 85, 101, 109] [10, 16, 43, 47, 84, 88, 92, 95, 111, 119] [20, 26, 53, 57, 94, 98, 102, 105, 121, 129] [30, 36, 63, 67, 104, 108, 112, 115, 131, 139] [40, 46, 73, 77, 114, 118, 122, 125, 141, 149] [50, 56, 83, 87, 124, 128, 132, 135, 151, 159] [60, 66, 93, 97, 134, 138, 142, 145, 161, 169] [1, 9, 70, 76, 103, 107, 144, 148, 152, 155] [11, 19, 80, 86, 113, 117, 154, 158, 162, 165] [2, 5, 21, 29, 90, 96, 123, 127, 164, 168] [4, 8, 12, 15, 31, 39, 100, 106, 133, 137] [14, 18, 22, 25, 41, 49, 110, 116, 143, 147] [24, 28, 32, 35, 51, 59, 120, 126, 153, 157] [34, 38, 42, 45, 61, 69, 130, 136, 163, 167] [3, 7, 44, 48, 52, 55, 71, 79, 140, 146] [13, 17, 54, 58, 62, 65, 81, 89, 150, 156] [23, 27, 64, 68, 72, 75, 91, 99, 160, 166] [0, 5, 12, 17, 43, 48, 154, 159, 161, 166] [1, 6, 10, 15, 22, 27, 53, 58, 164, 169] [4, 9, 11, 16, 20, 25, 32, 37, 63, 68] [14, 19, 21, 26, 30, 35, 42, 47, 73, 78] [24, 29, 31, 36, 40, 45, 52, 57, 83, 88] [34, 39, 41, 46, 50, 55, 62, 67, 93, 98] [44, 49, 51, 56, 60, 65, 72, 77, 103, 108] [54, 59, 61, 66, 70, 75, 82, 87, 113, 118] [64, 69, 71, 76, 80, 85, 92, 97, 123, 128] [74, 79, 81, 86, 90, 95, 102, 107, 133, 138] [84, 89, 91, 96, 100, 105, 112, 117, 143, 148] [94, 99, 101, 106, 110, 115, 122, 127, 153, 158] [104, 109, 111, 116, 120, 125, 132, 137, 163, 168] [3, 8, 114, 119, 121, 126, 130, 135, 142, 147] [13, 18, 124, 129, 131, 136, 140, 145, 152, 157] [23, 28, 134, 139, 141, 146, 150, 155, 162, 167] [2, 7, 33, 38, 144, 149, 151, 156, 160, 165] [0, 9, 81, 88, 124, 127, 142, 146, 163, 165] [3, 5, 10, 19, 91, 98, 134, 137, 152, 156] [13, 15, 20, 29, 101, 108, 144, 147, 162, 166] [2, 6, 23, 25, 30, 39, 111, 118, 154, 157] [12, 16, 33, 35, 40, 49, 121, 128, 164, 167] [4, 7, 22, 26, 43, 45, 50, 59, 131, 138] [14, 17, 32, 36, 53, 55, 60, 69, 141, 148] [24, 27, 42, 46, 63, 65, 70, 79, 151, 158] [34, 37, 52, 56, 73, 75, 80, 89, 161, 168] [1, 8, 44, 47, 62, 66, 83, 85, 90, 99] [11, 18, 54, 57, 72, 76, 93, 95, 100, 109] [21, 28, 64, 67, 82, 86, 103, 105, 110, 119] [31, 38, 74, 77, 92, 96, 113, 115, 120, 129] [41, 48, 84, 87, 102, 106, 123, 125, 130, 139] [51, 58, 94, 97, 112, 116, 133, 135, 140, 149] [61, 68, 104, 107, 122, 126, 143, 145, 150, 159] [71, 78, 114, 117, 132, 136, 153, 155, 160, 169] [0, 8, 73, 76, 104, 105, 151, 157, 162, 169] [2, 9, 10, 18, 83, 86, 114, 115, 161, 167] [1, 7, 12, 19, 20, 28, 93, 96, 124, 125] [11, 17, 22, 29, 30, 38, 103, 106, 134, 135] [21, 27, 32, 39, 40, 48, 113, 116, 144, 145] [31, 37, 42, 49, 50, 58, 123, 126, 154, 155] [41, 47, 52, 59, 60, 68, 133, 136, 164, 165] [4, 5, 51, 57, 62, 69, 70, 78, 143, 146] [14, 15, 61, 67, 72, 79, 80, 88, 153, 156] [24, 25, 71, 77, 82, 89, 90, 98, 163, 166] [3, 6, 34, 35, 81, 87, 92, 99, 100, 108] [13, 16, 44, 45, 91, 97, 102, 109, 110, 118] [23, 26, 54, 55, 101, 107, 112, 119, 120, 128] [33, 36, 64, 65, 111, 117, 122, 129, 130, 138] [43, 46, 74, 75, 121, 127, 132, 139, 140, 148] [53, 56, 84, 85, 131, 137, 142, 149, 150, 158] [63, 66, 94, 95, 141, 147, 152, 159, 160, 168]
Code ID 170-8-20 · download JSON · raw on GitHub