Bounds on the minimum distance of additive quantum codes
Bounds on [[97,80]]2
lower bound: | 4 |
upper bound: | 5 |
Construction
Construction of a [[97,80,4]] quantum code:
[1]: [[126, 114, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[92, 80, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 4, 6, 8, 21, 24, 28, 29, 30, 31, 35, 39, 42, 49, 50, 52, 55, 56, 58, 64, 68, 74, 75, 80, 85, 92, 95, 102, 104, 105, 106, 111, 112, 125 }
[3]: [[97, 80, 4]] quantum code over GF(2^2)
ExtendCode [2] by 5
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0|0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0]
[0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0|0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 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 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0|0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0]
[0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0|0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0|0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0|0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0|0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0|0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 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 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0|0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 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 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0|0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 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 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 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 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]
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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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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|1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 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 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 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