Bounds on the minimum distance of additive quantum codes
Bounds on [[202,178]]2
| lower bound: | 5 |
| upper bound: | 6 |
Construction
Construction of a [[202,178,5]] quantum code:
[1]: [[255, 231, 5]] quantum code over GF(2^2)
BCH code with parameters 255 5
[2]: [[202, 178, 5]] quantum code over GF(2^2)
Shortening of [1] at { 3, 7, 11, 14, 18, 22, 33, 34, 41, 53, 56, 60, 64, 68, 72, 75, 76, 83, 87, 94, 95, 102, 106, 110, 113, 117, 121, 129, 132, 133, 136, 140, 144, 148, 151, 159, 163, 167, 170, 177, 178, 182, 186, 189, 193, 197, 209, 212, 224, 228, 232, 247, 250 }
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 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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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024