Bounds on the minimum distance of additive quantum codes
Bounds on [[205,190]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[205,190,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[205, 191, 4]] quantum code over GF(2^2)
Shortening of [1] at { 3, 4, 8, 14, 41, 44, 54, 61, 70, 96, 101, 105, 115, 120, 121, 123, 124, 126, 140, 150, 162, 165, 194, 197, 203, 206, 220, 221, 222, 223, 224, 225, 226, 228, 230, 233, 235, 236, 237, 238, 241, 242, 244, 247, 248, 251, 252 }
[3]: [[205, 190, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 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