Bounds on the minimum distance of additive quantum codes
Bounds on [[84,60]]2
lower bound: | 6 |
upper bound: | 8 |
Construction
Construction of a [[84,60,6]] quantum code:
[1]: [[128, 105, 6]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[84, 61, 6]] quantum code over GF(2^2)
Shortening of [1] at { 2, 3, 4, 6, 16, 19, 21, 22, 24, 25, 26, 29, 30, 31, 34, 44, 45, 46, 50, 52, 56, 57, 63, 65, 66, 67, 72, 74, 76, 84, 86, 87, 89, 90, 93, 95, 98, 101, 108, 109, 112, 119, 123, 126 }
[3]: [[84, 60, 6]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0|0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1|0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0|0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1|0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1]
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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 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 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.
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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014