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[[232,62,12]] d ≤
n
232
k
62
d
12
kd²/n
38.483
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 12, d_Z ≤ 12 · 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 12 · witness weight 12 (claimed exact)
witness operator (support, 12 qubits)
[29, 34, 94, 109, 117, 132, 140, 151, 190, 205, 226, 228]
d_Z 12 · witness weight 12 (claimed exact)
witness operator (support, 12 qubits)
[0, 3, 50, 60, 63, 112, 118, 128, 157, 174, 177, 231]
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 8 · H_Z 8
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×232 (2,4)×2436 (3,3)×203 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 232 (2,4): 2436 (3,3): 203 (3,5): 33495 (3,7): 4872
trapping sets H_Z (1,3)×232 (2,4)×2436 (3,3)×203 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 232 (2,4): 2436 (3,3): 203 (3,5): 33495 (3,7): 4872

Construction & provenance

authors Maskara, Nishad
provenance literature baseline
construction Cyclic pair-partition CPM CSS construction (arXiv:2607.14091), Nishad Maskara's contributed instance pp_232_62_12_cw8_P29: lift size P=29, (J,L)=(3,8), n=8*29=232, 87 checks per side, column weight 3, row weight 8, Tanner girth 6/6. Circulant-exponent arrays (J x L, one per side): E_x = [[4, 15, 26, 20, 2, 2, 28, 17], [14, 5, 12, 7, 27, 14, 0, 11], [23, 24, 25, 2, 14, 18, 20, 21]], E_z = [[0, 24, 2, 7, 27, 18, 4, 26], [24, 16, 17, 25, 8, 3, 5, 22], [17, 4, 15, 26, 8, 13, 10, 1]]. Reconstruction per the archive's own description: for block (i,j), Hx[i*29 + r, j*29 + ((r - E_x[i][j]) mod 29)] = 1 for r=0..28; Hz likewise from E_z. H_X and H_Z here are taken verbatim from the authors' archive https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/contributed_codes/nishad_maskara/pp_232_62_12_cw8_P29.npz (sha256 260d1e15c179bd136560e557a6786bb240a4cfa8a5477347859b4b99c966dd6a), which is byte-identical to the certificate bundle's fixed input.
model classical construction (no AI model)
reference arXiv:2607.14091
date 2026
notes Literature baseline, seeded 2026-08-14. Listed as a Nishad Maskara contribution in the Okada-Kasai pair-partition CPM catalogue (arXiv:2607.14091; catalogue page updated 2026-08-13); the catalogue also lists an independent same-parameter instance PPS232 by Jong Yeon Lee with different circulant exponents, which is NOT this code and is not certified by the bundle below. The authors publish a machine-verified exact-distance certificate bundle for this instance (https://kasai.ict.eng.isct.ac.jp/pair_partition_cpm_css_codes_data/certificate_bundles_20260805/qc_232_62_12/certificate_bundle.tar.gz, status exact_distance_machine_verified in master_manifest.json), whose fixed input is byte-identical to the public npz: complete lower-bound coverage through weight 10 on both sides plus explicit weight-12 logicals, which are the witnesses here, re-verified in this repo (kernel membership, row-space non-membership). Marked exact on the strength of that public certificate; per board policy the entry still displays as an upper bound until this repo's own certification. Reproduction was validated end to end: the archive's H_X/H_Z match its documented exponent reconstruction exactly, are CSS-orthogonal, (3,8)-regular, with GF(2) ranks giving k=62. Discovery method of the contributed instance is undisclosed by the contributor; model provenance unknown.
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 87 (max weight 8) · Z-checks 87 (max weight 8)
H_X (87 checks, sparse supports)
[25, 43, 61, 96, 143, 172, 175, 215] [26, 44, 62, 97, 144, 173, 176, 216] [27, 45, 63, 98, 116, 145, 177, 217] [28, 46, 64, 99, 117, 146, 178, 218] [0, 47, 65, 100, 118, 147, 179, 219] [1, 48, 66, 101, 119, 148, 180, 220] [2, 49, 67, 102, 120, 149, 181, 221] [3, 50, 68, 103, 121, 150, 182, 222] [4, 51, 69, 104, 122, 151, 183, 223] [5, 52, 70, 105, 123, 152, 184, 224] [6, 53, 71, 106, 124, 153, 185, 225] [7, 54, 72, 107, 125, 154, 186, 226] [8, 55, 73, 108, 126, 155, 187, 227] [9, 56, 74, 109, 127, 156, 188, 228] [10, 57, 75, 110, 128, 157, 189, 229] [11, 29, 76, 111, 129, 158, 190, 230] [12, 30, 77, 112, 130, 159, 191, 231] [13, 31, 78, 113, 131, 160, 192, 203] [14, 32, 79, 114, 132, 161, 193, 204] [15, 33, 80, 115, 133, 162, 194, 205] [16, 34, 81, 87, 134, 163, 195, 206] [17, 35, 82, 88, 135, 164, 196, 207] [18, 36, 83, 89, 136, 165, 197, 208] [19, 37, 84, 90, 137, 166, 198, 209] [20, 38, 85, 91, 138, 167, 199, 210] [21, 39, 86, 92, 139, 168, 200, 211] [22, 40, 58, 93, 140, 169, 201, 212] [23, 41, 59, 94, 141, 170, 202, 213] [24, 42, 60, 95, 142, 171, 174, 214] [15, 53, 75, 109, 118, 160, 174, 221] [16, 54, 76, 110, 119, 161, 175, 222] [17, 55, 77, 111, 120, 162, 176, 223] [18, 56, 78, 112, 121, 163, 177, 224] [19, 57, 79, 113, 122, 164, 178, 225] [20, 29, 80, 114, 123, 165, 179, 226] [21, 30, 81, 115, 124, 166, 180, 227] [22, 31, 82, 87, 125, 167, 181, 228] [23, 32, 83, 88, 126, 168, 182, 229] [24, 33, 84, 89, 127, 169, 183, 230] [25, 34, 85, 90, 128, 170, 184, 231] [26, 35, 86, 91, 129, 171, 185, 203] [27, 36, 58, 92, 130, 172, 186, 204] [28, 37, 59, 93, 131, 173, 187, 205] [0, 38, 60, 94, 132, 145, 188, 206] [1, 39, 61, 95, 133, 146, 189, 207] [2, 40, 62, 96, 134, 147, 190, 208] [3, 41, 63, 97, 135, 148, 191, 209] [4, 42, 64, 98, 136, 149, 192, 210] [5, 43, 65, 99, 137, 150, 193, 211] [6, 44, 66, 100, 138, 151, 194, 212] [7, 45, 67, 101, 139, 152, 195, 213] [8, 46, 68, 102, 140, 153, 196, 214] [9, 47, 69, 103, 141, 154, 197, 215] [10, 48, 70, 104, 142, 155, 198, 216] [11, 49, 71, 105, 143, 156, 199, 217] [12, 50, 72, 106, 144, 157, 200, 218] [13, 51, 73, 107, 116, 158, 201, 219] [14, 52, 74, 108, 117, 159, 202, 220] [6, 34, 62, 114, 131, 156, 183, 211] [7, 35, 63, 115, 132, 157, 184, 212] [8, 36, 64, 87, 133, 158, 185, 213] [9, 37, 65, 88, 134, 159, 186, 214] [10, 38, 66, 89, 135, 160, 187, 215] [11, 39, 67, 90, 136, 161, 188, 216] [12, 40, 68, 91, 137, 162, 189, 217] [13, 41, 69, 92, 138, 163, 190, 218] [14, 42, 70, 93, 139, 164, 191, 219] [15, 43, 71, 94, 140, 165, 192, 220] [16, 44, 72, 95, 141, 166, 193, 221] [17, 45, 73, 96, 142, 167, 194, 222] [18, 46, 74, 97, 143, 168, 195, 223] [19, 47, 75, 98, 144, 169, 196, 224] [20, 48, 76, 99, 116, 170, 197, 225] [21, 49, 77, 100, 117, 171, 198, 226] [22, 50, 78, 101, 118, 172, 199, 227] [23, 51, 79, 102, 119, 173, 200, 228] [24, 52, 80, 103, 120, 145, 201, 229] [25, 53, 81, 104, 121, 146, 202, 230] [26, 54, 82, 105, 122, 147, 174, 231] [27, 55, 83, 106, 123, 148, 175, 203] [28, 56, 84, 107, 124, 149, 176, 204] [0, 57, 85, 108, 125, 150, 177, 205] [1, 29, 86, 109, 126, 151, 178, 206] [2, 30, 58, 110, 127, 152, 179, 207] [3, 31, 59, 111, 128, 153, 180, 208] [4, 32, 60, 112, 129, 154, 181, 209] [5, 33, 61, 113, 130, 155, 182, 210]
H_Z (87 checks, sparse supports)
[0, 34, 85, 109, 118, 156, 199, 206] [1, 35, 86, 110, 119, 157, 200, 207] [2, 36, 58, 111, 120, 158, 201, 208] [3, 37, 59, 112, 121, 159, 202, 209] [4, 38, 60, 113, 122, 160, 174, 210] [5, 39, 61, 114, 123, 161, 175, 211] [6, 40, 62, 115, 124, 162, 176, 212] [7, 41, 63, 87, 125, 163, 177, 213] [8, 42, 64, 88, 126, 164, 178, 214] [9, 43, 65, 89, 127, 165, 179, 215] [10, 44, 66, 90, 128, 166, 180, 216] [11, 45, 67, 91, 129, 167, 181, 217] [12, 46, 68, 92, 130, 168, 182, 218] [13, 47, 69, 93, 131, 169, 183, 219] [14, 48, 70, 94, 132, 170, 184, 220] [15, 49, 71, 95, 133, 171, 185, 221] [16, 50, 72, 96, 134, 172, 186, 222] [17, 51, 73, 97, 135, 173, 187, 223] [18, 52, 74, 98, 136, 145, 188, 224] [19, 53, 75, 99, 137, 146, 189, 225] [20, 54, 76, 100, 138, 147, 190, 226] [21, 55, 77, 101, 139, 148, 191, 227] [22, 56, 78, 102, 140, 149, 192, 228] [23, 57, 79, 103, 141, 150, 193, 229] [24, 29, 80, 104, 142, 151, 194, 230] [25, 30, 81, 105, 143, 152, 195, 231] [26, 31, 82, 106, 144, 153, 196, 203] [27, 32, 83, 107, 116, 154, 197, 204] [28, 33, 84, 108, 117, 155, 198, 205] [5, 42, 70, 91, 137, 171, 198, 210] [6, 43, 71, 92, 138, 172, 199, 211] [7, 44, 72, 93, 139, 173, 200, 212] [8, 45, 73, 94, 140, 145, 201, 213] [9, 46, 74, 95, 141, 146, 202, 214] [10, 47, 75, 96, 142, 147, 174, 215] [11, 48, 76, 97, 143, 148, 175, 216] [12, 49, 77, 98, 144, 149, 176, 217] [13, 50, 78, 99, 116, 150, 177, 218] [14, 51, 79, 100, 117, 151, 178, 219] [15, 52, 80, 101, 118, 152, 179, 220] [16, 53, 81, 102, 119, 153, 180, 221] [17, 54, 82, 103, 120, 154, 181, 222] [18, 55, 83, 104, 121, 155, 182, 223] [19, 56, 84, 105, 122, 156, 183, 224] [20, 57, 85, 106, 123, 157, 184, 225] [21, 29, 86, 107, 124, 158, 185, 226] [22, 30, 58, 108, 125, 159, 186, 227] [23, 31, 59, 109, 126, 160, 187, 228] [24, 32, 60, 110, 127, 161, 188, 229] [25, 33, 61, 111, 128, 162, 189, 230] [26, 34, 62, 112, 129, 163, 190, 231] [27, 35, 63, 113, 130, 164, 191, 203] [28, 36, 64, 114, 131, 165, 192, 204] [0, 37, 65, 115, 132, 166, 193, 205] [1, 38, 66, 87, 133, 167, 194, 206] [2, 39, 67, 88, 134, 168, 195, 207] [3, 40, 68, 89, 135, 169, 196, 208] [4, 41, 69, 90, 136, 170, 197, 209] [12, 54, 72, 90, 137, 161, 193, 231] [13, 55, 73, 91, 138, 162, 194, 203] [14, 56, 74, 92, 139, 163, 195, 204] [15, 57, 75, 93, 140, 164, 196, 205] [16, 29, 76, 94, 141, 165, 197, 206] [17, 30, 77, 95, 142, 166, 198, 207] [18, 31, 78, 96, 143, 167, 199, 208] [19, 32, 79, 97, 144, 168, 200, 209] [20, 33, 80, 98, 116, 169, 201, 210] [21, 34, 81, 99, 117, 170, 202, 211] [22, 35, 82, 100, 118, 171, 174, 212] [23, 36, 83, 101, 119, 172, 175, 213] [24, 37, 84, 102, 120, 173, 176, 214] [25, 38, 85, 103, 121, 145, 177, 215] [26, 39, 86, 104, 122, 146, 178, 216] [27, 40, 58, 105, 123, 147, 179, 217] [28, 41, 59, 106, 124, 148, 180, 218] [0, 42, 60, 107, 125, 149, 181, 219] [1, 43, 61, 108, 126, 150, 182, 220] [2, 44, 62, 109, 127, 151, 183, 221] [3, 45, 63, 110, 128, 152, 184, 222] [4, 46, 64, 111, 129, 153, 185, 223] [5, 47, 65, 112, 130, 154, 186, 224] [6, 48, 66, 113, 131, 155, 187, 225] [7, 49, 67, 114, 132, 156, 188, 226] [8, 50, 68, 115, 133, 157, 189, 227] [9, 51, 69, 87, 134, 158, 190, 228] [10, 52, 70, 88, 135, 159, 191, 229] [11, 53, 71, 89, 136, 160, 192, 230]
Code ID 232-62-12 · download JSON · raw on GitHub