Bounds on the minimum distance of additive quantum codes
Bounds on [[255,239]]2
| lower bound: | 4 |
| upper bound: | 4 |
Construction
Construction of a [[255,239,4]] quantum code:
[1]: [[286, 272, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[255, 241, 4]] quantum code over GF(2^2)
Shortening of [1] at { 29, 128, 165, 184, 190, 224, 232, 239, 240, 248, 251, 252, 253, 255, 258, 260, 262, 263, 264, 266, 269, 270, 271, 272, 279, 281, 282, 283, 284, 285, 286 }
[3]: [[255, 239, 4]] quantum code over GF(2^2)
Subcode of [2]
stabilizer matrix:
[1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1|0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 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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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024