Bounds on the minimum distance of additive quantum codes
Bounds on [[109,100]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[109,100,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[109, 100, 3]] quantum code over GF(2^2)
Shortening of [1] at { 1, 45, 46, 47, 50, 53, 54, 56, 57, 59, 61, 62, 63, 64, 68, 75, 76, 77, 78, 81, 82, 83, 86, 88, 92, 94, 97, 98, 103, 107, 115, 116, 118, 120, 121, 123, 124, 125, 128, 131, 132, 133, 137, 138, 139, 140, 141, 143, 148, 152, 154, 155, 157, 158, 161, 162, 165, 166, 167 }
stabilizer matrix:
[1 0 0 1 0 1 1 0 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 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0|0 1 1 0 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 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0]
[0 1 0 1 0 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 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1|0 0 1 1 0 0 1 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 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0]
[0 0 1 1 0 0 1 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 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1|0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1]
[0 0 0 0 1 1 1 0 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 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0|0 1 0 1 1 0 1 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 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 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 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 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 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1]
[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 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1|1 1 1 1 1 1 1 0 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 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 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 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 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 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 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 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 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 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 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 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]
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