Bounds on the minimum distance of additive quantum codes
Bounds on [[183,166]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[183,166,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[183, 169, 4]] quantum code over GF(2^2)
Shortening of [1] at { 11, 14, 18, 19, 20, 27, 29, 40, 42, 44, 51, 56, 63, 72, 77, 82, 84, 89, 94, 98, 103, 104, 105, 109, 112, 116, 119, 120, 121, 123, 124, 126, 129, 130, 131, 139, 140, 143, 153, 158, 171, 176, 184, 186, 187, 189, 190, 191, 195, 199, 218, 220, 226, 227, 229, 231, 234, 236, 238, 240, 242, 243, 244, 245, 246, 248, 250, 251, 252 }
[3]: [[183, 166, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 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