Bounds on the minimum distance of additive quantum codes
Bounds on [[128,53]]2
lower bound: | 15 |
upper bound: | 25 |
Construction
Construction of a [[128,53,15]] quantum code:
[1]: [[128, 56, 15]] quantum code over GF(2^2)
extended Quantum Twisted Code of length 128 with interval [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ] and parameter kappa 7
[2]: [[128, 53, 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 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 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 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0]
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last modified: 2024-04-15
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