Bounds on the minimum distance of additive quantum codes
Bounds on [[156,133]]2
| lower bound: | 4 |
| upper bound: | 6 |
Construction
Construction of a [[156,133,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[156, 142, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 4, 5, 8, 12, 15, 19, 21, 23, 24, 25, 28, 34, 37, 46, 48, 49, 61, 62, 65, 69, 71, 72, 79, 81, 83, 88, 92, 94, 98, 100, 103, 104, 105, 109, 114, 116, 118, 119, 120, 123, 128, 129, 130, 135, 139, 140, 144, 146, 149, 156, 158, 159, 161, 165, 169, 170, 173, 178, 182, 185, 186, 187, 190, 191, 194, 196, 197, 207, 208, 209, 213, 217, 218, 219, 221, 222, 223, 225, 231, 232, 234, 235, 238, 239, 240, 241, 242, 245, 246, 247, 249, 250, 251, 252 }
[3]: [[156, 133, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 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 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 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