Bounds on the minimum distance of additive quantum codes
Bounds on [[124,91]]2
lower bound: | 6 |
upper bound: | 10 |
Construction
Construction of a [[124,91,6]] quantum code:
[1]: [[168, 134, 7]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[124, 90, 7]] quantum code over GF(2^2)
Shortening of [1] at { 2, 8, 9, 10, 15, 16, 20, 22, 24, 25, 27, 36, 39, 40, 51, 66, 78, 80, 86, 87, 89, 92, 94, 95, 97, 99, 106, 112, 114, 116, 117, 120, 128, 132, 135, 139, 141, 142, 151, 153, 157, 158, 161, 165 }
[3]: [[123, 91, 6]] quantum code over GF(2^2)
Shortening of the stabilizer code of [2] at 124
[4]: [[124, 91, 6]] quantum code over GF(2^2)
ExtendCode [3] by 1
stabilizer matrix:
[1 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 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0]
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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