Bounds on the minimum distance of additive quantum codes
Bounds on [[125,109]]2
lower bound: | 4 |
upper bound: | 4 |
Construction
Construction of a [[125,109,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[123, 109, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 6, 8, 10, 12, 13, 15, 17, 19, 20, 23, 27, 29, 32, 33, 34, 37, 38, 39, 40, 41, 42, 45, 46, 50, 51, 53, 54, 56, 57, 58, 61, 68, 70, 73, 74, 75, 77, 78, 80, 82, 83, 86, 88, 90, 91, 93, 94, 95, 96, 98, 99, 103, 104, 111, 112, 113, 115, 116, 119, 120, 121, 123, 129, 130, 131, 132, 133, 134, 136, 138, 139, 140, 143, 144, 146, 147, 151, 152, 153, 154, 155, 162, 163, 165, 166, 168, 169, 170, 171, 175, 176, 178, 183, 185, 187, 189, 190, 191, 193, 194, 197, 200, 203, 204, 206, 209, 211, 215, 217, 219, 220, 221, 224, 225, 227, 228, 229, 230, 231, 232, 236, 237, 242, 244, 245, 246, 248 }
[3]: [[125, 109, 4]] quantum code over GF(2^2)
ExtendCode [2] by 2
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0|0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0]
[0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0|0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 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 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0]
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[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 1 0 0 0 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 1 0 1 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0]
last modified: 2006-04-03
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 even 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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Markus Grassl
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Last change: 23.10.2014