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[[100,53,2]] d ≤
n
100
k
53
d
2
kd²/n
2.12
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · 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 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[78, 79]
d_Z 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[78, 79]
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 4 · H_Z 4 (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 1–2 (mean 1.84) · H_Z 1–2 (mean 1.92)
trapping sets H_X (1,1)×16 (2,0)×50 (3,0)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 16 (1,2): 84 (2,0): 50 (2,1): 96 (2,2): 456 (3,0): 24 (3,1): 576 (3,2): 2976 (3,3): 192 (3,4): 544
trapping sets H_Z (1,1)×8 (2,0)×50 (3,1)×312 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 8 (1,2): 92 (2,0): 50 (2,1): 48 (2,2): 528 (3,1): 312 (3,2): 3576 (3,3): 96 (3,4): 672

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction C-DELETE-CHECK
model Beam 1.0 (claimed, not verified)
date 2026-10-20
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[100,53,2]] — C-DELETE-CHECK reduction

Direction & hypothesis

Deletion of a check from a board entry.

Evidence trail

Gate passes, board_advancing.

Tools

Model: Beam 1.0.

Parity checks

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