Bounds on the minimum distance of additive quantum codes
Bounds on [[124,115]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[124,115,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[124, 115, 3]] quantum code over GF(2^2)
Shortening of [1] at { 6, 15, 20, 24, 46, 48, 51, 55, 56, 57, 61, 64, 66, 69, 75, 76, 77, 78, 83, 87, 89, 98, 99, 102, 103, 104, 109, 113, 122, 124, 127, 128, 132, 138, 139, 142, 146, 151, 153, 156, 157, 158, 159, 160 }
stabilizer matrix:
[1 0 0 0 0 1 1 0 0 0 0 0 0 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 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0|0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0]
[0 1 0 0 1 1 1 0 0 0 0 0 0 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 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0|0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0]
[0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 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 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1|1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0]
[0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1|1 0 1 0 1 1 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 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1|1 1 1 1 1 1 1 0 0 0 0 0 0 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 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1|1 1 1 1 1 1 1 0 0 0 0 0 0 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 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 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 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1|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 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 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 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 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: 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
(codes@codetables.de).
Last change: 23.10.2014