Bounds on the minimum distance of additive quantum codes
Bounds on [[115,75]]2
lower bound: | 8 |
upper bound: | 12 |
Construction
Construction of a [[115,75,8]] quantum code:
[1]: [[111, 75, 8]] quantum code over GF(2^2)
constacyclic code generated by w*x^110 + w^2*x^109 + w^2*x^108 + w^2*x^107 + w^2*x^106 + w*x^105 + x^104 + w^2*x^102 + w*x^101 + x^97 + w^2*x^96 + w^2*x^95 + w^2*x^92 + w^2*x^91 + x^90 + x^87 + x^85 + w^2*x^84 + x^83 + x^82 + w^2*x^81 + w^2*x^80 + w*x^79 + w*x^78 + x^77 + w^2*x^76 + w^2*x^75 + w*x^74 + w*x^73 + w*x^72 + w*x^71 + x^70 + x^69 + w^2*x^68 + x^67 + w*x^65 + w^2*x^64 + x^63 + x^59 + x^58 + w*x^57 + w*x^55 + x^54 + w^2*x^53 + w*x^51 + w*x^48 + x^46 + x^45 + w*x^44 + w^2*x^43 + w^2*x^41 + w*x^40 + w^2*x^38 + w*x^37 + w^2*x^36 + w*x^35 + x^34 + x^33 + w^2*x^32 + w*x^31 + w^2*x^30 + w^2*x^29 + w*x^28 + w*x^26 + w*x^25 + x^22 + w*x^21 + w^2*x^19 + x^18 + 1 with shift constant w^2
[2]: [[115, 75, 8]] quantum code over GF(2^2)
ExtendCode [1] by 4
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 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0|1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 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.
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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014