Bounds on the minimum distance of additive quantum codes
Bounds on [[101,83]]2
lower bound: | 4 |
upper bound: | 6 |
Construction
Construction of a [[101,83,4]] quantum code:
[1]: [[122, 104, 5]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[102, 84, 5]] quantum code over GF(2^2)
Shortening of [1] at { 44, 62, 69, 79, 80, 82, 83, 92, 95, 96, 97, 102, 105, 107, 109, 110, 114, 115, 119, 122 }
[3]: [[101, 85, 4]] quantum code over GF(2^2)
Shortening of the stabilizer code of [2] at 102
[4]: [[101, 83, 4]] quantum code over GF(2^2)
Subcode of [3]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1|1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0|1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1|1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1]
[0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1|0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0|1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1]
[0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0|0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0|0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1]
[0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0|1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0|1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1|0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0|1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0|0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 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 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1|0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0|0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0|0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1]
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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 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 0 1]
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