Bounds on the minimum distance of additive quantum codes
Bounds on [[103,94]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[103,94,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[103, 94, 3]] quantum code over GF(2^2)
Shortening of [1] at { 3, 43, 46, 48, 49, 51, 53, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 71, 73, 76, 78, 81, 82, 85, 90, 92, 94, 95, 99, 106, 108, 109, 112, 115, 116, 118, 120, 123, 129, 130, 132, 133, 134, 135, 138, 140, 141, 143, 144, 145, 146, 147, 148, 153, 154, 156, 157, 158, 159, 161, 163, 164, 165, 166 }
stabilizer matrix:
[1 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 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0|0 0 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 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 0]
[0 1 0 0 1 1 0 0 0 1 1 0 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 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1|1 0 0 0 1 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 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0]
[0 0 1 0 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 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0|0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0]
[0 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 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1|1 0 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 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 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 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 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 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 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 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 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 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 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 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 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 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 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 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 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 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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