Bounds on the minimum distance of additive quantum codes
Bounds on [[176,154]]2
| lower bound: | 4 |
| upper bound: | 6 |
Construction
Construction of a [[176,154,4]] quantum code:
[1]: [[252, 238, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[176, 162, 4]] quantum code over GF(2^2)
Shortening of [1] at { 1, 9, 13, 14, 19, 27, 28, 39, 43, 44, 46, 51, 63, 66, 68, 75, 79, 83, 85, 88, 93, 94, 96, 99, 100, 102, 105, 110, 114, 115, 119, 120, 122, 123, 124, 126, 130, 132, 133, 134, 155, 159, 162, 164, 172, 174, 175, 182, 186, 191, 199, 208, 209, 210, 219, 222, 223, 224, 225, 226, 231, 235, 236, 237, 238, 239, 241, 242, 243, 245, 247, 248, 249, 250, 251, 252 }
[3]: [[176, 154, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024