Bounds on the minimum distance of additive quantum codes
Bounds on [[161,145]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[161,145,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[161, 147, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 2, 11, 14, 15, 17, 19, 20, 22, 24, 26, 28, 34, 36, 38, 45, 48, 51, 59, 63, 65, 75, 76, 77, 82, 89, 92, 93, 102, 105, 107, 109, 110, 111, 113, 114, 116, 119, 121, 122, 123, 124, 125, 126, 128, 130, 137, 139, 150, 156, 157, 159, 161, 168, 175, 182, 183, 184, 191, 192, 195, 197, 198, 203, 205, 206, 208, 209, 214, 216, 217, 220, 222, 224, 225, 226, 231, 232, 233, 234, 237, 238, 241, 242, 243, 244, 247, 249, 250, 251, 252 }
[3]: [[161, 145, 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 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1|0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 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