Bounds on the minimum distance of additive quantum codes
Bounds on [[117,20]]2
lower bound: | 18 |
upper bound: | 33 |
Construction
Construction of a [[117,20,18]] quantum code:
[1]: [[105, 21, 18]] quantum code over GF(2^2)
constacyclic code generated by x^42 + x^41 + w*x^40 + w^2*x^39 + w*x^38 + w^2*x^36 + w*x^33 + w^2*x^32 + x^30 + w*x^29 + x^28 + x^26 + w*x^24 + w^2*x^23 + w*x^22 + w*x^21 + x^20 + x^19 + w^2*x^18 + w*x^17 + w*x^16 + x^15 + w*x^14 + w*x^12 + x^11 + w^2*x^10 + x^9 + w^2*x^8 + x^7 + w^2*x^4 + x^2 + x + w with shift constant w
[2]: [[114, 21, 18]] quantum code over GF(2^2)
ExtendCode [1] by 9
[3]: [[114, 20, 18]] quantum code over GF(2^2)
Subcode of [2]
[4]: [[117, 20, 18]] quantum code over GF(2^2)
ExtendCode [3] by 3
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 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0|1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0]
last modified: 2022-08-02
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