[[170,16,10]] · QEC Challenge

[[170,16,10]] d =

170

kd²/n

9.412

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 10, d_Z = 10 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 10 · witness weight 10 (claimed upper_bound)

witness found by @FarLab · verify/ris_gpu --pair-depth 24 · found at 1.5×10⁷ trials · survived 3×10⁷ trials · 2026-08-19

witness operator (support, 10 qubits)

[1, 19, 34, 42, 62, 97, 99, 104, 110, 157]

d_Z 10 · witness weight 10 (claimed upper_bound)

witness found by @FarLab · verify/ris_gpu --pair-depth 24 · found at 1.5×10⁷ trials · survived 3×10⁷ trials · 2026-08-19

witness operator (support, 10 qubits)

[29, 102, 105, 120, 124, 138, 139, 154, 157, 169]

certificate exact, d = 10 · CryptoMiniSat 5.14.7 SAT

X: no logical < 10 exists; Z: no logical < 10 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 6 · H_Z 6

qubit degrees H_X 3 · H_Z 3

trapping sets H_X (1,3)×170 (2,4)×1275 (3,3)×170 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,3): 170 (2,4): 1275 (3,3): 170 (3,5): 12240 (3,7): 1700

trapping sets H_Z (1,3)×170 (2,4)×1275 (3,3)×170 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,3): 170 (2,4): 1275 (3,3): 170 (3,5): 12240 (3,7): 1700

Construction & provenance

authors @FarLab

provenance submitted through the challenge

novelty new parameter set claimed by submitter

construction Generalized bicycle (two-block) code on Z_85: H_X=[A|B], H_Z=[B^T|A^T], a(x)=x⁸+x³³+x⁴⁶, b(x)=x³+x¹⁸+x⁷⁰; g=gcd(a,b,x⁸⁵-1) irreducible of degree 8, k=2*deg(g)=16, row weight 6. Full circulant check sets kept (redundant rows carry the symmetry).

model Claude Fable 5 (claimed, not verified)

builds on arXiv:2203.17216, arXiv:2306.16400

date 2026-08-19

notes Orbit-structured GB search find; the full Tanner automorphism group acts with 3 orbits on the 16 canonical logical classes. Distance evidence: GPU deep-RIS 15M full-kernel pair trials x 2 seeds per side (CPU-verified witnesses) + sqetch 20Mx2 trials/side; nothing below 10 by any engine. Novelty basis: 2026-08-19 lit pass (Wang-Pryadko 2203.17216 = k=2 family; Lin-Pryadko 2306.16400 = n<=100; no zoo/board hits).

family generalized bicycle (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight ≤ 6 (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 6) · Z-checks 85 (max weight 6)

H_X (85 checks, sparse supports)

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

H_Z (85 checks, sparse supports)

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

Code ID 170-16-10 · download JSON · raw on GitHub