Bounds on the minimum distance of additive quantum codes
Bounds on [[50,32]]2
lower bound: | 5 |
upper bound: | 6 |
Construction
Construction of a [[50,32,5]] quantum code:
[1]: [[122, 104, 5]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[50, 32, 5]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 22, 23, 24, 25, 26, 28, 29, 31, 32, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 54, 55, 56, 58, 59, 62, 64, 65, 66, 69, 70, 71, 72, 75, 76, 78, 81, 82, 84, 87, 91, 93, 94, 97, 98, 100, 103, 104, 105, 106, 107, 113, 114, 115, 117, 121, 122 }
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1|1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1]
[0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1|0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1|0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1]
[0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1|0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1|0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0]
[0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0|0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1|0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1|0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1|0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0|0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 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 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0]
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 necessarily 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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Last change: 10.06.2024