Bounds on the minimum distance of additive quantum codes
Bounds on [[100,73]]2
lower bound: | 6 |
upper bound: | 8 |
Construction
Construction of a [[100,73,6]] quantum code:
[1]: [[128, 105, 6]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[96, 73, 6]] quantum code over GF(2^2)
Shortening of [1] at { 14, 58, 59, 60, 61, 63, 67, 69, 71, 81, 82, 84, 86, 88, 89, 90, 92, 94, 95, 98, 99, 100, 104, 106, 107, 111, 114, 118, 121, 124, 125, 128 }
[3]: [[100, 73, 6]] quantum code over GF(2^2)
ExtendCode [2] by 4
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0|1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 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 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 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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Last change: 23.10.2014