Bounds on the minimum distance of additive quantum codes
Bounds on [[94,70]]2
lower bound: | 6 |
upper bound: | 8 |
Construction
Construction of a [[94,70,6]] quantum code:
[1]: [[128, 105, 6]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[94, 71, 6]] quantum code over GF(2^2)
Shortening of [1] at { 1, 58, 60, 61, 68, 69, 70, 71, 73, 78, 83, 85, 87, 88, 90, 92, 95, 97, 98, 99, 102, 105, 106, 108, 109, 111, 112, 116, 118, 119, 120, 124, 126, 128 }
[3]: [[94, 70, 6]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1]
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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 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 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
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Last change: 23.10.2014