[[28,23,1]] · QEC Challenge

[[28,23,1]] d ≤

kd²/n

0.821429

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 1, d_Z ≤ 1 · w_X = 16, w_Z = 16 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 1 · witness weight 1 (claimed upper_bound)

witness operator (support, 1 qubits)

[3]

d_Z 1 · witness weight 1 (claimed upper_bound)

witness operator (support, 1 qubits)

[0]

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 15–16 (mean 15.5) · H_Z 15–16 (mean 15.667)

qubit degrees H_X 0–2 (mean 1.107) · H_Z 0–3 (mean 1.679)

trapping sets H_X (1,0)×5 (2,0)×77 (3,0)×448 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 5 (1,1): 15 (1,2): 8 (2,0): 77 (2,1): 120 (3,0): 448 (3,1): 511 (3,2): 448

trapping sets H_Z (1,0)×1 (2,0)×39 (3,0)×400 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,0): 1 (1,1): 11 (1,2): 12 (1,3): 4 (2,0): 39 (2,1): 136 (2,2): 92 (3,0): 400 (3,1): 911 (3,2): 700 (3,3): 312

Construction & provenance

authors @mathysrennela

provenance submitted through the challenge

novelty novelty not audited

construction code-calculus v0.2rc greedy gated

model Beam 1.0 (claimed, not verified)

date 2026-11-12

notes Generated by the priced construction calculus. Distance is reported only with witness-backed upper bounds; lower interval bounds are kept in the separate local ledger.

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

[[28,23,1]] — code-calculus v0.2rc greedy gated

Direction & hypothesis

Frontier gaps in the CSS track via greedy multi-step composition of C-DELETE-CHECK, E-PEEL, and E-PUNCTURE (code-calculus v0.2rc).

What was searched

CSS parents from codes/ with n <= 10, up to 3 greedy steps, budget 16 RIS trials per candidate, sector swap enabled, domination pruning. See the greedy gated campaign (code-calculus v0.2rc).

Evidence trail

Witness-backed upper bound validated by verify/validate_candidate.py (passed: true). Model: Beam 1.0.

Dead ends

Sector-swap-only, strict C-ADD-CHECK addition, and E-GLUE produced no board-advancing codes in this campaign.

Tools

code-calculus-dev (latest), research/kit coordination.

Reproduction

Run the greedy gated campaign (code-calculus v0.2rc) at n<=10, 3 steps, budget 16.

Parity checks

X-checks 2 (max weight 16) · Z-checks 3 (max weight 16)

H_X (2 checks, sparse supports)

[2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 24, 25, 26, 27] [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]

H_Z (3 checks, sparse supports)

[0, 1, 2, 4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27] [5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 23, 24, 25, 26, 27] [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]

Code ID 28-23-1 · download JSON · raw on GitHub