Bounds on the minimum distance of additive quantum codes
Bounds on [[77,50]]2
lower bound: | 6 |
upper bound: | 9 |
Construction
Construction of a [[77,50,6]] quantum code:
[1]: [[128, 105, 6]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[74, 51, 6]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 4, 9, 10, 11, 14, 16, 17, 19, 23, 24, 26, 27, 28, 30, 31, 33, 37, 40, 42, 48, 55, 57, 59, 61, 63, 64, 66, 67, 69, 71, 72, 76, 78, 80, 82, 84, 85, 87, 97, 99, 100, 103, 104, 105, 110, 113, 115, 116, 118, 124, 125, 126 }
[3]: [[74, 50, 6]] quantum code over GF(2^2)
Subcode of [2]
[4]: [[77, 50, 6]] quantum code over GF(2^2)
ExtendCode [3] by 3
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0|0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 0|0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0]
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last modified: 2006-04-03
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 even 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: 23.10.2014