Bounds on the minimum distance of additive quantum codes
Bounds on [[106,43]]2
lower bound: | 12 |
upper bound: | 21 |
Construction
Construction of a [[106,43,12]] quantum code:
[1]: [[105, 45, 12]] quantum code over GF(2^2)
constacyclic code generated by x^104 + x^102 + w^2*x^101 + w^2*x^100 + w*x^98 + w*x^96 + x^95 + w^2*x^94 + w*x^93 + w*x^92 + x^90 + w^2*x^89 + x^88 + w^2*x^86 + x^85 + w^2*x^84 + x^83 + w^2*x^82 + w*x^81 + w*x^80 + w^2*x^79 + w^2*x^77 + x^75 + x^13 with shift constant w
[2]: [[105, 43, 12]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[106, 43, 12]] quantum code over GF(2^2)
ExtendCode [2] 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 0 0 0 0 0 0 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 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0|1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0]
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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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014