Bounds on the minimum distance of additive quantum codes
Bounds on [[103,24]]2
lower bound: | 16 |
upper bound: | 27 |
Construction
Construction of a [[103,24,16]] quantum code:
[1]: [[92, 24, 16]] quantum code over GF(2^2)
ConstructionX using constacyclic codes [91,34], [91,33], and auxiliary code [1,1]
[2]: [[103, 24, 16]] quantum code over GF(2^2)
ExtendCode [1] by 11
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 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0|1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 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 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0|0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
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last modified: 2020-08-21
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