Bounds on the minimum distance of additive quantum codes
Bounds on [[105,49]]2
lower bound: | 11 |
upper bound: | 18 |
Construction
Construction of a [[105,49,11]] quantum code:
[1]: [[105, 51, 11]] quantum code over GF(2^2)
constacyclic code generated by x^104 + w^2*x^103 + x^102 + w^2*x^101 + w^2*x^100 + w^2*x^99 + x^98 + w*x^97 + x^96 + w^2*x^94 + w*x^93 + w^2*x^91 + w^2*x^88 + x^86 + w*x^85 + x^84 + w^2*x^82 + w^2*x^81 + x^80 + x^78 + x^54 with shift constant w
[2]: [[105, 49, 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 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1|0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 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 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0]
last modified: 2020-08-21
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