Bounds on the minimum distance of additive quantum codes
Bounds on [[82,2]]2
| lower bound: | 19 |
| upper bound: | 28 |
Construction
Construction type: EzermanGrasslLingOzbudakOzkaya
Construction of a [[82,2,19]] quantum code:
[1]: [[82, 2, 19]] quantum code over GF(2^2)
QuasiCyclicCode of length 82 stacked to height 2 with generating polynomials: x^11 + x^10 + w^2*x^9 + x^8 + w*x^7 + x^6 + x^5 + w*x^4 + x^3 + w^2*x^2 + x + 1, w*x^30 + w*x^29 + w^2*x^28 + x^27 + x^26 + x^25 + x^24 + w^2*x^23 + w*x^22 + w^2*x^20 + w*x^19 + x^18 + x^17 + w*x^15 + w^2*x^14 + w*x^12 + x^9 + x^7 + w*x^6 + x^5 + w^2*x^4 + x^3 + w*x + w^2, 0, x^31 + w*x^29 + w^2*x^28 + w^2*x^27 + x^26 + w^2*x^25 + x^24 + w^2*x^23 + w*x^22 + w^2*x^21 + x^20 + x^19 + w*x^17 + x^16 + x^15 + w*x^14 + x^12 + x^11 + w^2*x^10 + w*x^9 + w^2*x^8 + x^7 + w^2*x^6 + x^5 + w^2*x^4 + w^2*x^3 + w*x^2 + 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 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 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 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1]
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last modified: 2024-05-23
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 necessarily 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: 10.06.2024