Bounds on the minimum distance of additive quantum codes
Bounds on [[171,156]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[171,156,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[171, 157, 4]] quantum code over GF(2^2)
Shortening of [1] at { 5, 11, 13, 14, 23, 37, 38, 43, 47, 53, 55, 59, 65, 66, 68, 71, 76, 77, 87, 90, 92, 93, 96, 105, 107, 108, 110, 111, 112, 115, 116, 117, 120, 124, 125, 126, 133, 135, 136, 142, 146, 151, 154, 157, 158, 159, 166, 168, 171, 179, 185, 193, 195, 199, 200, 206, 210, 214, 215, 218, 220, 222, 223, 224, 225, 226, 227, 228, 231, 233, 234, 235, 236, 239, 240, 242, 245, 246, 247, 248, 250 }
[3]: [[171, 156, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1|0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 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