Bounds on the minimum distance of additive quantum codes
Bounds on [[152,136]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[152,136,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[152, 138, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 5, 6, 7, 17, 18, 22, 26, 28, 30, 31, 32, 33, 36, 37, 39, 40, 47, 49, 52, 55, 56, 61, 62, 68, 70, 72, 74, 77, 81, 82, 87, 89, 91, 92, 93, 97, 98, 113, 114, 116, 119, 120, 121, 122, 123, 129, 130, 133, 134, 135, 138, 139, 142, 143, 149, 150, 153, 155, 160, 164, 165, 166, 173, 177, 180, 183, 184, 185, 187, 193, 204, 206, 209, 211, 214, 216, 217, 218, 219, 220, 222, 224, 226, 228, 229, 232, 234, 237, 238, 239, 240, 241, 244, 245, 246, 247, 248, 250, 252 }
[3]: [[152, 136, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0|0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0|1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 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