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[[17,9,2]] d ≤
n
17
k
9
d
2
kd²/n
2.11765
w
5
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 2, d_Z ≤ 2 · w_X = 5, w_Z = 5 (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)
[8, 12]
d_Z 2 · witness weight 2 (claimed upper_bound)
witness operator (support, 2 qubits)
[0, 1]
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 acyclic · H_Z acyclic (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 5 · H_Z 5
qubit degrees H_X 1–4 (mean 1.176) · H_Z 1–4 (mean 1.176)
trapping sets H_X (1,1)×16 (2,0)×24 (3,1)×16 (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 (1,4): 1 (2,0): 24 (2,3): 16 (3,1): 16 (3,2): 96 (3,4): 24
trapping sets H_Z (1,1)×16 (2,0)×24 (3,1)×16 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 16 (1,4): 1 (2,0): 24 (2,3): 16 (3,1): 16 (3,2): 96 (3,4): 24

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction C-ADD-CHECK strict improvement (code calculus v0.2rc): added one check killing every minimum-weight logical of parent codes/17-10-1.json
model Beam 1.0 (claimed, not verified)
date 2026-11-07
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

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

[[17,9,2]] — C-ADD-CHECK strict improvement of 17-10-1

Direction & hypothesis

Convert the parent (codes/17-10-1.json, d=2) by C-ADD-CHECK strict improvement (Proposition 18.3, code calculus v0.2rc): every minimum-weight logical class of the parent is killed by the added check, so the child's distance is at least d+1.

What was searched

For d=1 parents: the minimum-weight classes are the bare (weight-1) logicals, enumerated in O(n); the added check support is their union (plus a GF(2)-solved parity correction when the bare set alone is inadmissible). For d=2 parents: the weight-2 logical classes are enumerated (O(n^2)) and a greedy set-cover over admissible checks kills them within the check budget.

Evidence trail

  • Parent: codes/17-10-1.json.
  • Child witnesses: inherited from the parent where still valid, plus

    • fresh witnesses at the child's distance found by bounded scan.

  • Verified by verify/validate_candidate.py (passed: true), including the

    • random-seed refutation pass.

Dead ends

Parents whose bare-logical set gave an inadmissible check support were fixed by a parity correction solved over GF(2); parents whose system is inconsistent have no single-check fix and were skipped. Multi-check greedy at d=2 succeeds on only a minority of parents (the weight-2 class count grows quickly with n).

Tools

Model: Beam 1.0. Author: @MathysRennela. Construction calculus v0.2rc.

Reproduction

Start from codes/17-10-1.json; add the recorded check to obtain this entry.

Parity checks

X-checks 4 (max weight 5) · Z-checks 4 (max weight 5)
H_X (4 checks, sparse supports)
[0, 1, 2, 3, 16] [4, 5, 6, 7, 16] [8, 9, 10, 11, 16] [12, 13, 14, 15, 16]
H_Z (4 checks, sparse supports)
[0, 4, 8, 12, 16] [1, 5, 9, 13, 16] [2, 6, 10, 14, 16] [3, 7, 11, 15, 16]
Code ID 17-9-2 · download JSON · raw on GitHub