Bounds on the minimum distance of additive quantum codes
Bounds on [[77,3]]2
lower bound: | 17 |
upper bound: | 26 |
Construction
Construction of a [[77,3,17]] quantum code:
[1]: [[80, 0, 20]] self-dual quantum code over GF(2^2)
QuasiCyclicCode of length 80 with generating polynomials: 1, w*x^36 + w^2*x^35 + x^34 + w*x^33 + x^32 + x^30 + w*x^29 + x^28 + w*x^27 + w^2*x^25 + w*x^24 + w*x^23 + w*x^21 + w*x^20 + x^19 + x^18 + w^2*x^17 + x^16 + x^15 + x^14 + w^2*x^13 + w*x^12 + w*x^11 + x^9 + x^5 + w*x^4 + x^3 + x + w
[2]: [[77, 3, 17]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at { 78, 79, 80 }
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 1 0 0 0 1 1|0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 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 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1]
last modified: 2011-07-04
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