Bounds on the minimum distance of additive quantum codes
Bounds on [[115,106]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[115,106,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[115, 106, 3]] quantum code over GF(2^2)
Shortening of [1] at { 13, 46, 48, 49, 52, 56, 58, 60, 63, 67, 68, 76, 79, 82, 84, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 101, 102, 103, 115, 116, 120, 122, 123, 125, 127, 128, 129, 130, 133, 134, 135, 136, 138, 141, 143, 144, 145, 149, 150, 151, 155, 164, 165 }
stabilizer matrix:
[1 0 0 0 0 1 1 1 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 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0|0 0 1 0 1 1 0 1 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 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0]
[0 1 0 0 1 0 1 1 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 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0|0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 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 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0]
[0 0 1 0 1 1 0 1 0 0 1 1 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 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1|1 0 1 1 0 1 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 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0]
[0 0 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 1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1|1 0 1 0 1 0 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 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0]
[0 0 0 0 0 0 0 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 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1|1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0]
[0 0 0 0 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 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1|1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 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 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 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 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 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 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 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 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 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 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]
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