Bounds on the minimum distance of additive quantum codes
Bounds on [[19,8]]2
lower bound: | 4 |
upper bound: | 4 |
Construction
Construction of a [[19,8,4]] quantum code:
[1]: [[17, 9, 4]] quantum code over GF(2^2)
Construction from a stored generator matrix
[2]: [[17, 8, 4]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[19, 8, 4]] quantum code over GF(2^2)
ExtendCode [2] by 2
stabilizer matrix:
[1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0|0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0]
[0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0|1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0]
[0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0|0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0]
[0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0|0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0]
[0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0|0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0|0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0]
[0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0|0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0]
[0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0|0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0]
[0 0 0 0 1 0 0 0 0 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 1 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 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
last modified: 2005-06-27
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 necessarily 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: 10.06.2024