Bounds on the minimum distance of additive quantum codes
Bounds on [[125,93]]2
lower bound: | 6 |
upper bound: | 10 |
Construction
Construction of a [[125,93,6]] quantum code:
[1]: [[168, 134, 7]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[126, 92, 7]] quantum code over GF(2^2)
Shortening of [1] at { 16, 17, 21, 26, 27, 28, 30, 34, 36, 40, 41, 42, 45, 50, 54, 66, 72, 73, 74, 78, 82, 85, 88, 91, 94, 102, 108, 120, 123, 130, 131, 134, 136, 138, 139, 140, 144, 150, 152, 158, 164, 165 }
[3]: [[125, 93, 6]] quantum code over GF(2^2)
Shortening of the stabilizer code of [2] at 126
stabilizer matrix:
[1 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 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0|0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1]
last modified: 2006-04-03
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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014