Bounds on the minimum distance of additive quantum codes
Bounds on [[100,0]]2
lower bound: | 22 |
upper bound: | 34 |
Construction
Construction of a [[100,0,22]] quantum code:
[1]: [[100, 0, 22]] self-dual quantum code over GF(2^2)
QuasiCyclicCode of length 100 with generating polynomials: x^33, w*x^49 + w*x^48 + x^47 + w^2*x^46 + w*x^45 + x^44 + x^43 + w*x^42 + w^2*x^41 + x^39 + w^2*x^37 + x^36 + w*x^35 + w^2*x^34 + w^2*x^33 + x^32 + w^2*x^31 + w^2*x^30 + x^28 + w^2*x^27 + w^2*x^26 + w*x^24 + x^21 + x^20 + w*x^19 + w*x^18 + w*x^17 + x^16 + w*x^15 + w^2*x^14 + x^13 + x^12 + x^11 + x^10 + w*x^9 + x^8 + w^2*x^7 + x^6 + w*x^5 + w*x^4 + w*x^3 + w^2*x + 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0]
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last modified: 2016-07-13
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