Bounds on the minimum distance of additive quantum codes
Bounds on [[88,79]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[88,79,3]] quantum code:
[1]: [[128, 119, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[88, 79, 3]] quantum code over GF(2^2)
Shortening of [1] at { 2, 7, 8, 10, 18, 22, 25, 26, 27, 28, 29, 32, 35, 39, 40, 43, 48, 55, 61, 63, 69, 77, 78, 82, 83, 92, 95, 98, 100, 102, 104, 105, 108, 111, 116, 121, 123, 124, 126, 127 }
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0]
[0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0|0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1]
[0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1|0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1|0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0]
[0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0|0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0|0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1]
[0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1|0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0|0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 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|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 1 1 1 1 1 1 1 1 1 1 1 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