Bounds on the minimum distance of additive quantum codes
Bounds on [[75,19]]2
lower bound: | 12 |
upper bound: | 20 |
Construction
Construction of a [[75,19,12]] quantum code:
[1]: [[73, 19, 12]] quantum code over GF(2^2)
cyclic code of length 73 with generating polynomial x^72 + x^71 + x^70 + w*x^69 + w^2*x^68 + w*x^67 + x^66 + w*x^65 + w^2*x^64 + w^2*x^63 + x^62 + x^61 + x^60 + w^2*x^59 + x^58 + w^2*x^57 + x^56 + w^2*x^52 + w*x^49 + w^2*x^47 + w*x^46 + x^45 + w^2*x^44 + x^43 + w*x^42 + x^41 + w^2*x^40 + w^2*x^38 + w^2*x^37 + w^2*x^35 + w*x^33 + w*x^32 + w^2*x^30 + w^2*x^29 + x^27 + x^26 + x^25 + 1
[2]: [[75, 19, 12]] quantum code over GF(2^2)
ExtendCode [1] by 2
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 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0|1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 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 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]
last modified: 2008-02-16
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