Bounds on the minimum distance of additive quantum codes
Bounds on [[93,0]]2
lower bound: | 20 |
upper bound: | 32 |
Construction
Construction of a [[93,0,20]] quantum code:
[1]: [[93, 0, 20]] self-dual quantum code over GF(2^2)
cyclic code of length 93 with generating polynomial x^92 + w*x^91 + w^2*x^90 + x^89 + x^88 + x^87 + w^2*x^86 + w*x^85 + w*x^84 + x^82 + w*x^80 + w^2*x^79 + x^77 + w^2*x^76 + x^75 + w*x^74 + x^73 + x^71 + x^69 + w*x^68 + x^67 + w^2*x^66 + x^65 + w^2*x^63 + w*x^62 + x^60 + w*x^58 + w*x^57 + w^2*x^56 + x^55 + x^54 + x^53 + w^2*x^52 + w*x^51 + x^50 + w*x^49 + w
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 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 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 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 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0]
last modified: 2008-02-21
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.
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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014