Bounds on the minimum distance of additive quantum codes
Bounds on [[107,98]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[107,98,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[107, 98, 3]] quantum code over GF(2^2)
Shortening of [1] at { 9, 41, 42, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 59, 62, 63, 66, 69, 70, 71, 77, 78, 79, 82, 84, 85, 92, 93, 98, 99, 101, 103, 104, 106, 107, 113, 114, 117, 119, 122, 123, 126, 131, 134, 135, 136, 137, 140, 143, 144, 146, 148, 149, 150, 152, 156, 157, 159, 163, 167 }
stabilizer matrix:
[1 0 0 0 0 1 1 1 0 0 0 0 0 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 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0|0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0]
[0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 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 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1|0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0]
[0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1|1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1]
[0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0|0 1 0 1 0 1 0 1 0 0 0 0 0 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 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 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 0 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 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 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 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 1 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 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 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 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 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