Bounds on the minimum distance of additive quantum codes
Bounds on [[127,118]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[127,118,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[127, 118, 3]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 6, 7, 10, 12, 19, 22, 26, 27, 28, 33, 34, 35, 39, 56, 72, 77, 93, 97, 101, 103, 105, 107, 108, 111, 114, 117, 123, 126, 130, 133, 137, 140, 145, 146, 151, 152, 160, 163, 165 }
stabilizer matrix:
[1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0|0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0]
[0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1|1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0]
[0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0|0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0]
[0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1|1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1|1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0|0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 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 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1|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 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 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 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 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 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 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 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 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