Bounds on the minimum distance of additive quantum codes
Bounds on [[118,85]]2
lower bound: | 7 |
upper bound: | 10 |
Construction
Construction of a [[118,85,7]] quantum code:
[1]: [[113, 85, 7]] quantum code over GF(2^2)
cyclic code of length 113 with generating polynomial w*x^111 + x^110 + w^2*x^108 + w*x^107 + w*x^106 + w*x^105 + w^2*x^103 + x^102 + x^101 + x^100 + w*x^99 + w*x^98 + x^97 + w*x^96 + w^2*x^94 + x^92 + w^2*x^91 + w*x^89 + x^88 + w^2*x^87 + w^2*x^86 + x^85 + w*x^84 + w^2*x^83 + w*x^81 + w*x^80 + w^2*x^79 + w*x^78 + w*x^77 + w*x^75 + w*x^74 + w*x^73 + x^72 + w*x^70 + w^2*x^67 + w*x^65 + w*x^64 + w*x^63 + w*x^62 + w^2*x^60 + w*x^57 + x^55 + w*x^54 + w*x^53 + w*x^52 + w*x^50 + w*x^49 + w^2*x^48 + w*x^47 + w*x^46 + w^2*x^44 + w*x^43 + x^42 + w^2*x^41 + w^2*x^40 + x^39 + w*x^38 + w^2*x^36 + x^35 + w^2*x^33 + w*x^31 + x^30 + w*x^29 + w*x^28 + x^27 + x^26 + x^25 + w^2*x^24 + w*x^22 + w*x^21 + w*x^20 + w^2*x^19 + x^17 + w*x^16 + x^14 + 1
[2]: [[118, 85, 7]] quantum code over GF(2^2)
ExtendCode [1] by 5
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 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0|1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 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