Bounds on the minimum distance of additive quantum codes
Bounds on [[100,74]]2
lower bound: | 6 |
upper bound: | 8 |
Construction
Construction of a [[100,74,6]] quantum code:
[1]: [[128, 105, 6]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[98, 75, 6]] quantum code over GF(2^2)
Shortening of [1] at { 1, 9, 58, 61, 62, 63, 64, 67, 72, 74, 80, 81, 83, 84, 86, 88, 98, 102, 105, 108, 109, 111, 114, 115, 118, 120, 121, 124, 125, 127 }
[3]: [[98, 74, 6]] quantum code over GF(2^2)
Subcode of [2]
[4]: [[100, 74, 6]] quantum code over GF(2^2)
ExtendCode [3] by 2
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 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 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0|0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 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 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 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
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Last change: 23.10.2014