Bounds on the minimum distance of additive quantum codes
Bounds on [[75,0]]2
| lower bound: | 18 |
| upper bound: | 26 |
Construction
Construction of a [[75,0,18]] quantum code:
[1]: [[75, 0, 18]] self-dual quantum code over GF(2^2)
cyclic code of length 75 with generating polynomial x^74 + x^73 + w*x^72 + w*x^69 + w*x^68 + w*x^67 + w^2*x^66 + w*x^65 + w^2*x^63 + x^61 + w^2*x^59 + x^58 + w*x^57 + w^2*x^56 + w^2*x^55 + x^54 + w*x^53 + w*x^52 + w*x^50 + w^2*x^49 + w^2*x^47 + x^46 + w^2*x^45 + w*x^44 + w*x^43 + x^42 + w^2*x^41 + x^40 + x^39 + w^2*x^38 + w*x
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 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 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 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1]
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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 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0]
last modified: 2008-02-11
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