Bounds on the minimum distance of additive quantum codes
Bounds on [[92,65]]2
lower bound: | 6 |
upper bound: | 8 |
Construction
Construction of a [[92,65,6]] quantum code:
[1]: [[128, 105, 6]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[88, 65, 6]] quantum code over GF(2^2)
Shortening of [1] at { 2, 19, 20, 26, 27, 29, 33, 35, 37, 40, 43, 48, 50, 51, 54, 55, 56, 58, 59, 60, 61, 66, 68, 73, 74, 77, 79, 80, 89, 90, 91, 100, 102, 113, 118, 120, 121, 122, 123, 128 }
[3]: [[92, 65, 6]] quantum code over GF(2^2)
ExtendCode [2] by 4
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0|0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0|0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0]
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[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0]
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
(codes@codetables.de).
Last change: 23.10.2014