Bounds on the minimum distance of additive quantum codes
Bounds on [[111,102]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[111,102,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[111, 102, 3]] quantum code over GF(2^2)
Shortening of [1] at { 24, 43, 45, 47, 48, 50, 51, 58, 60, 62, 66, 67, 70, 71, 72, 73, 77, 78, 79, 80, 83, 84, 85, 86, 89, 90, 91, 96, 97, 98, 100, 101, 102, 110, 113, 114, 117, 118, 119, 121, 122, 124, 135, 143, 144, 146, 147, 150, 152, 155, 156, 159, 160, 162, 164, 165, 168 }
stabilizer matrix:
[1 0 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 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0|0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0]
[0 1 0 0 1 0 1 1 0 0 0 0 0 0 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 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0|0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0]
[0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0|1 0 1 1 0 1 0 0 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 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 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 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0|1 0 1 0 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 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 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 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1|1 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 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 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 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 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 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 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 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 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 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 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 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 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 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]
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