Bounds on the minimum distance of additive quantum codes
Bounds on [[174,160]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[174,160,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[174, 160, 4]] quantum code over GF(2^2)
Shortening of [1] at { 11, 12, 15, 17, 20, 22, 27, 29, 30, 33, 34, 35, 37, 41, 44, 46, 49, 64, 69, 70, 71, 72, 76, 78, 86, 89, 104, 105, 107, 110, 113, 115, 119, 120, 121, 123, 125, 126, 136, 138, 140, 142, 147, 148, 149, 159, 162, 173, 179, 182, 185, 193, 197, 200, 201, 202, 217, 218, 219, 221, 224, 225, 227, 228, 230, 231, 232, 233, 234, 235, 236, 237, 238, 241, 242, 246, 251, 252 }
stabilizer matrix:
[1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1|1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0]
[0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 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 0 1 1 1 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1|0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1]
[0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 1|0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1]
[0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1|0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 1|0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1]
[0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1|0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0]
[0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0|0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0]
[0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0|0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0]
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[0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 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 1 1 1 1 1 1 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 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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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