Bounds on the minimum distance of additive quantum codes
Bounds on [[147,130]]2
| lower bound: | 4 |
| upper bound: | 5 |
Construction
Construction of a [[147,130,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[147, 133, 4]] quantum code over GF(2^2)
Shortening of [1] at { 2, 5, 6, 8, 10, 13, 17, 19, 27, 30, 31, 32, 33, 34, 35, 36, 38, 40, 43, 46, 48, 49, 51, 52, 59, 62, 68, 69, 73, 75, 77, 78, 79, 81, 87, 88, 92, 93, 97, 98, 108, 110, 113, 114, 116, 118, 119, 121, 122, 123, 124, 125, 130, 134, 135, 140, 142, 144, 147, 150, 152, 153, 154, 156, 157, 158, 162, 169, 173, 175, 179, 181, 182, 183, 186, 191, 195, 199, 200, 208, 209, 213, 214, 215, 217, 223, 224, 225, 226, 227, 228, 229, 232, 233, 235, 236, 237, 238, 239, 240, 245, 247, 249, 250, 252 }
[3]: [[147, 130, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1|0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1|1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0]
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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