Bounds on the minimum distance of additive quantum codes
Bounds on [[112,0]]2
lower bound: | 22 |
upper bound: | 38 |
Construction
Construction of a [[112,0,22]] quantum code:
[1]: [[114, 0, 24]] self-dual quantum code over GF(2^2)
ConstructionX using cyclic codes [113,57], [113,56], and auxiliary code [1,1]
[2]: [[112, 0, 23]] self-dual quantum code over GF(2^2)
Puncturing of [1] at { 113 .. 114 }
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0]
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last modified: 2020-09-22
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