Bounds on the minimum distance of additive quantum codes
Bounds on [[89,80]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[89,80,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[89, 80, 3]] quantum code over GF(2^2)
Shortening of [1] at { 17, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 60, 61, 62, 64, 68, 71, 72, 74, 76, 77, 78, 80, 81, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 95, 96, 97, 99, 101, 102, 103, 107, 110, 111, 112, 114, 116, 117, 118, 119, 123, 126, 128, 129, 130, 131, 132, 134, 136, 137, 138, 139, 140, 141, 146, 147, 149, 150, 151, 152, 153, 157, 160, 161, 162, 166, 167 }
stabilizer matrix:
[1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1|0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1]
[0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0|0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0]
[0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1|1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1]
[0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1|1 0 1 0 1 0 1 0 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 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 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 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 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 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 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 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1|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 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 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 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 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 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 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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]
last modified: 2008-08-05
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