Bounds on the minimum distance of additive quantum codes
Bounds on [[166,145]]2
| lower bound: | 4 |
| upper bound: | 6 |
Construction
Construction of a [[166,145,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[166, 152, 4]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 7, 12, 18, 19, 21, 27, 28, 35, 42, 43, 45, 48, 54, 58, 60, 61, 62, 67, 71, 78, 82, 83, 91, 92, 100, 103, 104, 112, 113, 114, 116, 119, 120, 121, 122, 125, 128, 130, 131, 133, 142, 145, 155, 159, 162, 163, 173, 177, 180, 181, 182, 183, 188, 190, 192, 193, 204, 207, 208, 209, 214, 219, 220, 222, 226, 228, 230, 231, 233, 234, 235, 237, 238, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 252 }
[3]: [[166, 145, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 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 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 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