Author: Weilei Zeng
This is a database of CSS codes, with n=4..30 and distances up to 5/6. All parameters were saved, including k, x, and z stabilizers, in JSON format. Stabilizer matrices were saved in Matrix Market Format.
When doing research related to CSS codes, small sample codes are needed to get quick results or to construct product codes. A database for codes with various parameters will ease this process a lot.
The folder codes has enough codes to generate the table. For more codes with duplicated parameters and other versions, please download from the GitHub release page or Google Drive
File list
| Filename | Size | Codes count | Content |
|---|---|---|---|
| sample.tar | 45M | 34,582 | only i1 |
| css-codes-v1.0.tar | 382M | 400,000+ | i0 - i9 |
Folder structure:
Sample file name (replace n6k4d1-x1z1dx1dz1-1 for <code>):
codes/i1/n6/k4/n6k4d1-x1z1dx1dz1-1Gx.mmcodes/i1/n6/k4/n6k4d1-x1z1dx1dz1-1Gz.mmcodes/i1/n6/k4/n6k4d1-x1z1dx1dz1-1.json
Format: replace <> for allowed parameters
codes/i<>/n<>/k<>/n<>k<>d<>-x<>z<>dx<>dz<>-<>.jsoncodes/i<>/n<>/k<>/n<>k<>d<>-x<>z<>dx<>dz<>-<>Gx.mmcodes/i<>/n<>/k<>/n<>k<>d<>-x<>z<>dx<>dz<>-<>Gz.mm
The data comply with Matrix Market and JSON format and can be extracted by any IO tools. Here we provide sample code in Python. Check out the notebook dataIO.ipynb
version 1.4.1, (run3 as of Sept 27, 2023)
Disclaimer: This table displays collected statistics from heavy random sampling. Theoretically, it is only the lower distance bound for each (k,d) set, though it matches the maximum distance for most entries.
Row index for n, column index for k, and element for d
[n,k,d] table
n=0: [ 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7]
n=1: [ ]
n=2: [ ]
n=3: [ ]
n=4: [ 2 2 ]
n=5: [ 2 2 1 ]
n=6: [ 2 2 2 2 ]
n=7: [ 3 2 2 2 1 ]
n=8: [ 3 2 2 2 2 2 ]
n=9: [ 3 2 2 2 2 2 1 ]
n=10: [ 3 2 2 2 2 2 2 1 ]
n=11: [ 3 3 2 2 2 2 2 2 1 ]
n=12: [ 3 3 3 2 2 2 2 2 2 1 ]
n=13: [ 3 3 3 2 2 2 2 2 2 2 1 ]
n=14: [ 3 3 3 3 3 2 2 2 2 2 2 1 ]
n=15: [ 4 3 3 3 3 2 2 2 2 2 2 2 1 ]
n=16: [ 4 3 3 3 3 2 2 2 2 2 2 2 2 1 ]
n=17: [ 4 4 3 3 3 3 3 2 2 2 2 2 2 2 1 ]
n=18: [ 4 4 3 3 3 3 3 2 2 2 2 2 2 2 1 1 ]
n=19: [ 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 1 1 ]
n=20: [ 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 1 1 ]
n=21: [ 4 4 4 4 4 3 3 3 3 2 2 2 2 2 2 2 2 1 1 ]
n=22: [ 5 4 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 1 1 ]
n=23: [ 5 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 1 1 ]
n=24: [ 5 4 4 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 ]
n=25: [ 5 4 4 4 4 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 ]
n=26: [ 5 5 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 ]
n=27: [ 5 5 4 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 ]
n=28: [ 5 5 5 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1 ]
n=29: [ 5 5 5 5 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1]
n=30: [ 5 5 5 5 4 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1]
total number of codes: 17825
Algorithm
for n=4..30
for rx=1..<n-2>
for rz=1..<n-rx-2>
generate random matrix Hx
solve for dual matrix G such that Hx*G^T=0
get Hz by concatenating G into rz rows
estimate parameters n,k,d,dx,dz，
if unique
save CSS code defined by parity check matrices Hx and Hz,
end if
end for
end for
end for
This database complies with the MIT License. It is open to use and build upon it.