Bounds on the minimum distance of additive quantum codes
Bounds on [[118,87]]2
lower bound: | 6 |
upper bound: | 9 |
Construction
Construction of a [[118,87,6]] quantum code:
[1]: [[117, 87, 6]] quantum code over GF(2^2)
cyclic code of length 117 with generating polynomial w*x^115 + w^2*x^113 + w^2*x^112 + w^2*x^110 + w^2*x^108 + x^106 + w^2*x^105 + x^104 + w*x^103 + w^2*x^100 + w^2*x^97 + w*x^96 + w^2*x^95 + x^94 + w^2*x^93 + w*x^92 + x^91 + x^90 + x^89 + w*x^88 + x^87 + w^2*x^86 + w^2*x^85 + w*x^84 + w*x^83 + w*x^82 + w*x^81 + w*x^79 + w^2*x^78 + w^2*x^77 + w*x^76 + w^2*x^74 + x^73 + x^72 + w*x^71 + w^2*x^70 + w^2*x^69 + x^67 + w*x^66 + x^65 + w^2*x^64 + w*x^63 + w^2*x^61 + w*x^59 + w^2*x^58 + x^57 + w^2*x^56 + w*x^55 + w^2*x^54 + w^2*x^53 + x^52 + w^2*x^51 + w*x^50 + w*x^49 + w*x^48 + w^2*x^47 + w^2*x^46 + w^2*x^45 + w*x^44 + w^2*x^43 + w^2*x^42 + w*x^40 + w^2*x^38 + w^2*x^35 + w^2*x^33 + x^30 + w^2*x^28 + w*x^26 + w^2*x^25 + x^24 + w*x^21 + w*x^16 + w^2*x^15 + 1
[2]: [[118, 87, 6]] quantum code over GF(2^2)
ExtendCode [1] by 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 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0|1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0]
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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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014