Bounds on the minimum distance of additive quantum codes
Bounds on [[130,111]]2
| lower bound: | 4 |
| upper bound: | 6 |
Construction
Construction of a [[130,111,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[130, 116, 4]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 10, 11, 12, 13, 14, 17, 19, 21, 23, 24, 28, 30, 32, 33, 39, 40, 41, 42, 45, 48, 50, 51, 52, 55, 57, 58, 60, 61, 63, 66, 67, 71, 72, 74, 75, 76, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 90, 91, 93, 98, 99, 100, 104, 105, 106, 107, 108, 109, 115, 117, 121, 126, 127, 130, 131, 132, 133, 134, 138, 140, 142, 145, 146, 147, 149, 150, 153, 155, 156, 157, 158, 165, 167, 169, 174, 175, 177, 182, 183, 186, 189, 197, 199, 201, 202, 204, 205, 209, 210, 211, 214, 216, 217, 218, 219, 220, 223, 225, 230, 231, 233, 234, 235, 236, 238, 241, 242, 244, 248, 252 }
[3]: [[130, 111, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1]
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last modified: 2009-02-08
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