Bounds on the minimum distance of additive quantum codes
Bounds on [[195,181]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[195,181,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[195, 181, 4]] quantum code over GF(2^2)
Shortening of [1] at { 20, 23, 29, 42, 46, 62, 71, 79, 91, 93, 102, 114, 116, 119, 120, 121, 122, 123, 124, 126, 128, 130, 139, 141, 144, 150, 181, 183, 187, 206, 208, 209, 215, 218, 220, 221, 223, 224, 225, 226, 227, 228, 229, 231, 235, 237, 238, 241, 242, 244, 246, 247, 248, 249, 250, 251, 252 }
stabilizer matrix:
[1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1|1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0]
[0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1|0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1]
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last modified: 2009-02-08
Notes
- All codes establishing the lower bounds where constructed using MAGMA.
- Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
- For n>100, the upper bounds on qubit codes are weak (and not necessarily monotone in k).
- Some additional information can be found in the book by Nebe, Rains, and Sloane.
- My apologies to all authors that have contributed codes to this table for not giving specific credits.
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Last change: 10.06.2024