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[[42,8,3]] d =
n
42
k
8
d
3
kd²/n
1.714
w
6

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Distance

d_X 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[4, 11, 18]
d_Z 3 · witness weight 3 (claimed upper_bound)
witness operator (support, 3 qubits)
[0, 3, 15]
certificate exact, d = 3 · scipy/HiGHS MILP
X: no logical < 3 exists; Z: no logical < 3 exists

Construction & provenance

authors Wang, Renren and Pryadko, Leonid P.
provenance literature baseline
construction Generalized bicycle code, circulant size 21, a(x) = 1 + x3 + x6 + x12, b(x) = 1 + x7.
model classical construction (no AI model)
reference arXiv:2203.17216
date 2022-03-31
notes Distance d=3 from arXiv:2203.17216; witness here is a decoder-found logical operator of that weight (upper bound).
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 21 · Z-checks 21
H_X (21 checks, sparse supports)
[0, 3, 6, 12, 21, 28] [1, 4, 7, 13, 22, 29] [2, 5, 8, 14, 23, 30] [3, 6, 9, 15, 24, 31] [4, 7, 10, 16, 25, 32] [5, 8, 11, 17, 26, 33] [6, 9, 12, 18, 27, 34] [7, 10, 13, 19, 28, 35] [8, 11, 14, 20, 29, 36] [0, 9, 12, 15, 30, 37] [1, 10, 13, 16, 31, 38] [2, 11, 14, 17, 32, 39] [3, 12, 15, 18, 33, 40] [4, 13, 16, 19, 34, 41] [5, 14, 17, 20, 21, 35] [0, 6, 15, 18, 22, 36] [1, 7, 16, 19, 23, 37] [2, 8, 17, 20, 24, 38] [0, 3, 9, 18, 25, 39] [1, 4, 10, 19, 26, 40] [2, 5, 11, 20, 27, 41]
H_Z (21 checks, sparse supports)
[0, 14, 21, 30, 36, 39] [1, 15, 22, 31, 37, 40] [2, 16, 23, 32, 38, 41] [3, 17, 21, 24, 33, 39] [4, 18, 22, 25, 34, 40] [5, 19, 23, 26, 35, 41] [6, 20, 21, 24, 27, 36] [0, 7, 22, 25, 28, 37] [1, 8, 23, 26, 29, 38] [2, 9, 24, 27, 30, 39] [3, 10, 25, 28, 31, 40] [4, 11, 26, 29, 32, 41] [5, 12, 21, 27, 30, 33] [6, 13, 22, 28, 31, 34] [7, 14, 23, 29, 32, 35] [8, 15, 24, 30, 33, 36] [9, 16, 25, 31, 34, 37] [10, 17, 26, 32, 35, 38] [11, 18, 27, 33, 36, 39] [12, 19, 28, 34, 37, 40] [13, 20, 29, 35, 38, 41]
raw submission JSON