Bounds on the minimum distance of additive quantum codes
Bounds on [[81,0]]2
| lower bound: | 19 |
| upper bound: | 28 |
Construction
Construction type: Grassl
Construction of a [[81,0,19]] quantum code:
[1]: [[82, 0, 20]] self-dual quantum code over GF(2^2)
QuasiCyclicCode of length 82 with generating polynomials: x^27, w^2*x^39 + w^2*x^38 + w^2*x^37 + w^2*x^36 + x^34 + x^33 + w*x^32 + x^30 + x^29 + w^2*x^27 + w^2*x^26 + x^25 + x^24 + w*x^23 + w^2*x^21 + w*x^20 + w*x^17 + w^2*x^16 + w*x^14 + w*x^13 + w^2*x^11 + w*x^10 + x^9 + w^2*x^7 + w*x^6 + w^2*x^5 + x^3 + x^2 + w^2*x
[2]: [[81, 1, 19]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at 82
[3]: [[81, 0, 19]] self-dual quantum code over GF(2^2)
Subcode of [2]
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 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 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 0 1|1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1]
last modified: 2011-07-06
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