Bounds on the minimum distance of additive quantum codes
Bounds on [[207,190]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[207,190,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[207, 193, 4]] quantum code over GF(2^2)
Shortening of [1] at { 4, 19, 24, 27, 35, 68, 70, 112, 114, 116, 118, 120, 122, 124, 125, 126, 147, 161, 163, 165, 177, 181, 206, 208, 209, 211, 221, 223, 225, 226, 227, 228, 229, 231, 236, 237, 239, 241, 243, 246, 247, 248, 249, 250, 251 }
[3]: [[207, 190, 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 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 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