Bounds on the minimum distance of additive quantum codes
Bounds on [[65,0]]2
lower bound: | 16 |
upper bound: | 23 |
Construction
Construction of a [[65,0,16]] quantum code:
[1]: [[65, 0, 16]] self-dual quantum code over GF(2^2)
cyclic code of length 65 with generating polynomial x^62 + w^2*x^58 + x^57 + w*x^56 + w*x^55 + x^54 + x^53 + w*x^51 + w*x^50 + w^2*x^49 + x^48 + w^2*x^47 + w*x^46 + w*x^45 + x^43 + x^42 + w*x^41 + w*x^40 + x^39 + w^2*x^38 + x^34 + x^31 + 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 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 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 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 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 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 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1]
[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|1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 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 1 0 0 0 0 0|1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 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 1 0 0 0 0|0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 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 1 0 0 0|1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 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 1 0 0|1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 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 1 0|0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 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 1|0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 0]
last modified: 2009-02-08
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