Bounds on the minimum distance of additive quantum codes
Bounds on [[91,31]]2
lower bound: | 13 |
upper bound: | 21 |
Construction
Construction of a [[91,31,13]] quantum code:
[1]: [[91, 31, 13]] quantum code over GF(2^2)
cyclic code of length 91 with generating polynomial w*x^90 + w*x^89 + w*x^88 + w^2*x^87 + w^2*x^86 + w*x^85 + x^84 + w^2*x^83 + w^2*x^80 + x^79 + w^2*x^77 + w^2*x^76 + x^75 + x^73 + w*x^72 + x^71 + x^70 + x^69 + x^68 + w^2*x^67 + w^2*x^66 + w^2*x^65 + x^64 + x^63 + w*x^62 + w*x^61 + w^2*x^60 + x^59 + w*x^58 + x^57 + w*x^56 + x^55 + w*x^54 + w^2*x^52 + w*x^50 + x^49 + x^47 + x^45 + w^2*x^44 + w*x^42 + x^41 + x^40 + x^39 + x^38 + w^2*x^37 + x^36 + w*x^35 + x^34 + w*x^33 + w^2*x^32 + x^30 + 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 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1|1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 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 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1|1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 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 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1|1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1]
last modified: 2006-04-03
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