Bounds on the minimum distance of additive quantum codes
Bounds on [[122,113]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[122,113,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[122, 113, 3]] quantum code over GF(2^2)
Shortening of [1] at { 1, 3, 4, 7, 8, 10, 15, 28, 29, 31, 37, 38, 41, 46, 52, 53, 56, 57, 60, 62, 69, 70, 75, 79, 81, 84, 85, 92, 94, 95, 96, 98, 100, 103, 104, 106, 110, 112, 117, 120, 121, 122, 131, 151, 166, 168 }
stabilizer matrix:
[1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 0|1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1]
[0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0|1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1]
[0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0|0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1]
[0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1|1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1]
[0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0|0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0]
[0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1|1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0|0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1|0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
last modified: 2008-08-05
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