Bounds on the minimum distance of additive quantum codes
Bounds on [[97,88]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[97,88,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[97, 88, 3]] quantum code over GF(2^2)
Shortening of [1] at { 4, 41, 42, 43, 45, 47, 49, 51, 52, 54, 57, 59, 61, 64, 65, 66, 67, 68, 69, 70, 74, 76, 78, 79, 80, 81, 82, 83, 85, 86, 89, 92, 93, 94, 98, 100, 101, 103, 109, 111, 114, 115, 119, 120, 121, 123, 125, 127, 128, 129, 130, 132, 133, 135, 137, 138, 139, 140, 145, 146, 148, 149, 150, 151, 152, 153, 155, 159, 160, 161, 165 }
stabilizer matrix:
[1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 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 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0|0 0 1 1 1 0 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 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0]
[0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1|1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1]
[0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0|0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 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 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1|1 0 1 1 0 1 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 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0]
[0 0 0 0 0 0 0 1 0 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 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 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 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 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 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0|1 1 1 1 1 1 1 0 0 0 0 0 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 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 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 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1|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 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 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 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]
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