Bounds on the minimum distance of additive quantum codes
Bounds on [[91,72]]2
lower bound: | 5 |
upper bound: | 6 |
Construction
Construction of a [[91,72,5]] quantum code:
[1]: [[122, 104, 5]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[90, 72, 5]] quantum code over GF(2^2)
Shortening of [1] at { 3, 72, 73, 75, 76, 78, 80, 83, 85, 86, 87, 88, 92, 93, 96, 97, 98, 99, 100, 101, 103, 106, 108, 109, 110, 111, 112, 115, 116, 118, 119, 121 }
[3]: [[91, 72, 5]] quantum code over GF(2^2)
ExtendCode [2] by 1
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0|0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0|0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 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 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0|0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0|0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0|1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0|0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0|1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0|0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0|0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0|1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0|1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0|1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0|1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0|1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 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 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0|1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0|1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0|0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 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 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0|1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014