Bounds on the minimum distance of additive quantum codes
Bounds on [[113,104]]2
lower bound: | 3 |
upper bound: | 3 |
Construction
Construction of a [[113,104,3]] quantum code:
[1]: [[168, 159, 3]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[113, 104, 3]] quantum code over GF(2^2)
Shortening of [1] at { 2, 41, 42, 43, 45, 53, 54, 55, 63, 67, 74, 76, 77, 79, 80, 82, 83, 85, 86, 89, 91, 93, 95, 98, 99, 103, 105, 108, 110, 111, 112, 113, 114, 115, 116, 120, 123, 125, 127, 133, 136, 140, 141, 142, 143, 148, 151, 152, 153, 154, 156, 158, 159, 160, 161 }
stabilizer matrix:
[1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0|0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0]
[0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1|1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0]
[0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1|1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0]
[0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0|0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0|1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0|1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 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 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1|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 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 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 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 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 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 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 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]
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