← back to the board
[[80,8,8]] d =
n
80
k
8
d
8
kd²/n
6.4
w
8

Share this result

Distance

d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[6, 9, 13, 14, 22, 55, 70, 76]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[10, 16, 31, 40, 42, 69, 77, 78]
certificate exact, d = 8 · scipy/HiGHS MILP
X: no logical < 8 exists; Z: no logical < 8 exists

Construction & provenance

authors Lin, Hsiang-Ku and Pryadko, Leonid P.
provenance literature baseline
construction Two-block group algebra (2BGA) code over C_8 x C_5: a={1, s r4}, b={1, r, r2, s, s3 r, s2 r6} (Lin & Pryadko, arXiv:2306.16400, Table 1).
model classical construction (no AI model)
reference arXiv:2306.16400
date 2023
notes Literature baseline (arXiv:2306.16400, Lin & Pryadko, 28 Jun 2023). Two-block group algebra code reconstructed from the published group presentation; distance d=10 taken from the paper's Table 1 and certified by an explicit non-stabilizer witness on each side (regenerated via the research kit's RIS search). Literature novelty confirmed by manual cross-check: arXiv:2306.16400 Table 1 explicitly reports the [[80,8,10]] parameters with W=6 (reconstructed checks have weight 8). The verifier's 'literature novelty UNVERIFIED' label is by-design (validate_candidate.py performs no literature lookup) and is intentionally not overridden.
family 2BGA coset (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (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 40 · Z-checks 40
H_X (40 checks, sparse supports)
[0, 24, 40, 44, 53, 70, 75, 77] [1, 20, 40, 41, 54, 71, 76, 78] [2, 21, 41, 42, 50, 72, 77, 79] [3, 22, 42, 43, 51, 73, 75, 78] [4, 23, 43, 44, 52, 74, 76, 79] [5, 29, 40, 42, 45, 49, 58, 75] [6, 25, 41, 43, 45, 46, 59, 76] [7, 26, 42, 44, 46, 47, 55, 77] [8, 27, 40, 43, 47, 48, 56, 78] [9, 28, 41, 44, 48, 49, 57, 79] [10, 34, 40, 45, 47, 50, 54, 63] [11, 30, 41, 46, 48, 50, 51, 64] [12, 31, 42, 47, 49, 51, 52, 60] [13, 32, 43, 45, 48, 52, 53, 61] [14, 33, 44, 46, 49, 53, 54, 62] [15, 39, 45, 50, 52, 55, 59, 68] [16, 35, 46, 51, 53, 55, 56, 69] [17, 36, 47, 52, 54, 56, 57, 65] [18, 37, 48, 50, 53, 57, 58, 66] [19, 38, 49, 51, 54, 58, 59, 67] [4, 20, 50, 55, 57, 60, 64, 73] [0, 21, 51, 56, 58, 60, 61, 74] [1, 22, 52, 57, 59, 61, 62, 70] [2, 23, 53, 55, 58, 62, 63, 71] [3, 24, 54, 56, 59, 63, 64, 72] [9, 25, 55, 60, 62, 65, 69, 78] [5, 26, 56, 61, 63, 65, 66, 79] [6, 27, 57, 62, 64, 66, 67, 75] [7, 28, 58, 60, 63, 67, 68, 76] [8, 29, 59, 61, 64, 68, 69, 77] [14, 30, 43, 60, 65, 67, 70, 74] [10, 31, 44, 61, 66, 68, 70, 71] [11, 32, 40, 62, 67, 69, 71, 72] [12, 33, 41, 63, 65, 68, 72, 73] [13, 34, 42, 64, 66, 69, 73, 74] [19, 35, 48, 65, 70, 72, 75, 79] [15, 36, 49, 66, 71, 73, 75, 76] [16, 37, 45, 67, 72, 74, 76, 77] [17, 38, 46, 68, 70, 73, 77, 78] [18, 39, 47, 69, 71, 74, 78, 79]
H_Z (40 checks, sparse supports)
[0, 1, 5, 8, 10, 32, 40, 61] [1, 2, 6, 9, 11, 33, 41, 62] [2, 3, 5, 7, 12, 34, 42, 63] [3, 4, 6, 8, 13, 30, 43, 64] [0, 4, 7, 9, 14, 31, 44, 60] [5, 6, 10, 13, 15, 37, 45, 66] [6, 7, 11, 14, 16, 38, 46, 67] [7, 8, 10, 12, 17, 39, 47, 68] [8, 9, 11, 13, 18, 35, 48, 69] [5, 9, 12, 14, 19, 36, 49, 65] [2, 10, 11, 15, 18, 20, 50, 71] [3, 11, 12, 16, 19, 21, 51, 72] [4, 12, 13, 15, 17, 22, 52, 73] [0, 13, 14, 16, 18, 23, 53, 74] [1, 10, 14, 17, 19, 24, 54, 70] [7, 15, 16, 20, 23, 25, 55, 76] [8, 16, 17, 21, 24, 26, 56, 77] [9, 17, 18, 20, 22, 27, 57, 78] [5, 18, 19, 21, 23, 28, 58, 79] [6, 15, 19, 22, 24, 29, 59, 75] [12, 20, 21, 25, 28, 30, 41, 60] [13, 21, 22, 26, 29, 31, 42, 61] [14, 22, 23, 25, 27, 32, 43, 62] [10, 23, 24, 26, 28, 33, 44, 63] [11, 20, 24, 27, 29, 34, 40, 64] [17, 25, 26, 30, 33, 35, 46, 65] [18, 26, 27, 31, 34, 36, 47, 66] [19, 27, 28, 30, 32, 37, 48, 67] [15, 28, 29, 31, 33, 38, 49, 68] [16, 25, 29, 32, 34, 39, 45, 69] [0, 22, 30, 31, 35, 38, 51, 70] [1, 23, 31, 32, 36, 39, 52, 71] [2, 24, 32, 33, 35, 37, 53, 72] [3, 20, 33, 34, 36, 38, 54, 73] [4, 21, 30, 34, 37, 39, 50, 74] [0, 3, 5, 27, 35, 36, 56, 75] [1, 4, 6, 28, 36, 37, 57, 76] [0, 2, 7, 29, 37, 38, 58, 77] [1, 3, 8, 25, 38, 39, 59, 78] [2, 4, 9, 26, 35, 39, 55, 79]
raw submission JSON