Bounds on the minimum distance of additive quantum codes
Bounds on [[91,82]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[91,82,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[91, 82, 3]] quantum code over GF(2^2)
Shortening of [1] at { 2, 7, 8, 11, 12, 15, 17, 18, 19, 20, 21, 22, 24, 26, 27, 28, 29, 30, 31, 36, 37, 39, 40, 41, 42, 43, 45, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 81, 83, 84, 85, 87, 88, 91, 92, 93, 96, 98, 99, 104, 105, 106, 107, 109, 114, 115, 118, 121, 122, 125, 138, 168 }
stabilizer matrix:
[1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0|0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1|1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1]
[0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1|1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1]
[0 0 0 1 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 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0|0 1 1 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1]
[0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 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 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 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 0 1 1 1 1 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1|1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 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 1 0 1 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0|0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 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 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1|0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]
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