Bounds on the minimum distance of additive quantum codes
Bounds on [[146,129]]2
| lower bound: | 4 |
| upper bound: | 5 |
Construction
Construction of a [[146,129,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[146, 132, 4]] quantum code over GF(2^2)
Shortening of [1] at { 2, 4, 6, 8, 9, 10, 11, 15, 16, 19, 22, 23, 27, 28, 29, 32, 34, 43, 44, 45, 48, 53, 54, 56, 57, 58, 61, 64, 69, 70, 74, 75, 76, 77, 79, 80, 81, 85, 86, 87, 90, 92, 94, 95, 97, 98, 99, 114, 118, 120, 123, 124, 127, 132, 133, 135, 137, 138, 140, 141, 144, 146, 147, 149, 154, 156, 157, 161, 163, 166, 168, 171, 172, 174, 177, 178, 180, 181, 187, 190, 194, 195, 196, 199, 200, 202, 204, 207, 210, 211, 216, 217, 218, 219, 221, 222, 225, 230, 231, 232, 234, 236, 241, 242, 246, 252 }
[3]: [[146, 129, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0|1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 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