Bounds on the minimum distance of additive quantum codes
Bounds on [[107,29]]2
lower bound: | 14 |
upper bound: | 27 |
Construction
Construction of a [[107,29,14]] quantum code:
[1]: [[108, 30, 15]] quantum code over GF(2^2)
Code found by Dastbaste & Lisonek using Construction X from constacyclic codes [105, 69, 14]_4 and [105, 66, 16]_4
Construction from a stored generator matrix
[2]: [[108, 29, 15]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[107, 29, 14]] quantum code over GF(2^2)
Puncturing of [2] at { 108 }
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 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1|0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0|1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 1]
last modified: 2022-08-02
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