Bounds on the minimum distance of additive quantum codes
Bounds on [[105,24]]2
lower bound: | 16 |
upper bound: | 28 |
Construction
Construction of a [[105,24,16]] quantum code:
[1]: [[105, 27, 16]] quantum code over GF(2^2)
constacyclic code generated by w^2*x^104 + w^2*x^103 + w*x^102 + x^101 + x^100 + x^99 + x^98 + x^97 + w*x^96 + x^94 + w^2*x^93 + w*x^91 + w*x^90 + w^2*x^89 + w^2*x^88 + w*x^86 + w^2*x^83 + x^82 + x^81 + w*x^74 + x^73 + x^72 + x^71 + x^70 + w^2*x^68 + x^67 + w^2*x^66 + x^8 with shift constant w
[2]: [[105, 24, 16]] 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 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 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0|0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 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 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 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0|0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 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 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 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0|1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0]
last modified: 2020-07-31
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