Bounds on the minimum distance of additive quantum codes
Bounds on [[79,10]]2
lower bound: | 15 |
upper bound: | 24 |
Construction
Construction of a [[79,10,15]] quantum code:
[1]: [[79, 11, 15]] quantum code over GF(2^2)
random linear code
Construction from a stored generator matrix
[2]: [[79, 10, 15]] quantum code over GF(2^2)
Subcode of [1]
stabilizer matrix:
[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 1 0 1 1 1 0 1 1 0 1|0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1]
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last modified: 2022-11-27
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 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