Bounds on the minimum distance of additive quantum codes
Bounds on [[119,110]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[119,110,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[119, 110, 3]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 7, 9, 10, 11, 12, 16, 21, 26, 29, 30, 32, 44, 50, 69, 89, 92, 93, 95, 100, 101, 104, 106, 107, 108, 110, 116, 119, 120, 125, 127, 128, 130, 135, 136, 141, 146, 147, 149, 150, 151, 152, 155, 157, 159, 160, 163, 164 }
stabilizer matrix:
[1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1|0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0]
[0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0|0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0]
[0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1|0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0]
[0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0|0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1|1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0]
[0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1|1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 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 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1|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 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 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 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 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 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 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