Bounds on the minimum distance of additive quantum codes
Bounds on [[85,34]]2
lower bound: | 11 |
upper bound: | 18 |
Construction
Construction of a [[85,34,11]] quantum code:
[1]: [[85, 37, 11]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomial w*x^83 + w^2*x^82 + w*x^81 + w^2*x^80 + w*x^77 + w*x^75 + w^2*x^74 + w^2*x^73 + x^72 + w^2*x^71 + w^2*x^70 + x^69 + x^67 + x^66 + w*x^65 + w^2*x^63 + x^62 + x^61 + w^2*x^60 + w*x^59 + w^2*x^58 + w*x^57 + w*x^56 + w^2*x^55 + x^54 + w^2*x^53 + w*x^51 + w*x^49 + w*x^48 + w^2*x^46 + w^2*x^45 + x^43 + w*x^40 + x^39 + w^2*x^38 + x^37 + w^2*x^36 + x^35 + w*x^33 + w^2*x^31 + x^30 + w^2*x^29 + w^2*x^27 + w*x^26 + x^24 + 1
[2]: [[85, 34, 11]] quantum code over GF(2^2)
Subcode of [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 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1|1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0]
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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 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 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 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 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 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