Bounds on the minimum distance of additive quantum codes
Bounds on [[15,0]]2
lower bound: | 6 |
upper bound: | 6 |
Construction
Construction of a [[15,0,6]] quantum code:
[1]: [[15, 0, 6]] self-dual quantum code over GF(2^2)
cyclic code of length 15 with generating polynomial x^14 + w^2*x^13 + w^2*x^12 + x^11 + w^2*x^10 + w^2*x^9 + x^8 + w*x^7 + w
stabilizer matrix:
[1 0 0 0 0 0 0 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 1 1 1 1 1 1 1|1 0 0 0 0 0 0 1 0 1 1 0 1 1 0]
[0 1 0 0 0 0 0 0 1 0 1 1 0 0 1|0 0 0 0 0 0 0 1 0 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 1 1 1 0 0 1 1|0 1 0 0 0 0 0 0 1 1 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 0 1 1 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 1 1 1 0 1 0 1|0 0 1 0 0 0 0 0 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 1 1 1 1 0 0|0 0 0 0 0 0 0 1 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 1|0 0 0 1 0 0 0 1 0 0 0 1 1 1 1]
[0 0 0 0 1 0 0 0 1 1 0 0 0 0 1|0 0 0 0 0 0 0 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 1 1 0 1 1 1|0 0 0 0 1 0 0 1 1 0 0 1 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 1|0 0 0 0 0 0 0 1 1 1 0 1 0 1 1]
[0 0 0 0 0 0 0 0 1 0 1 0 1 1 1|0 0 0 0 0 1 0 0 1 0 1 1 0 0 0]
[0 0 0 0 0 0 1 0 0 1 1 0 0 1 0|0 0 0 0 0 0 0 1 1 1 1 1 1 0 0]
[0 0 0 0 0 0 0 0 1 1 0 0 1 1 1|0 0 0 0 0 0 1 0 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 0 0 1|0 0 0 0 0 0 0 0 1 1 1 1 1 1 0]
last modified: 2006-04-17
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 necessarily 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: 10.06.2024