Bounds on the minimum distance of additive quantum codes
Bounds on [[84,5]]2
lower bound: | 18 |
upper bound: | 27 |
Construction
Construction of a [[84,5,18]] quantum code:
[1]: [[85, 9, 19]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomial x^38 + w*x^37 + w*x^36 + w^2*x^35 + w*x^34 + x^33 + w^2*x^30 + x^29 + w*x^28 + x^26 + w*x^25 + w*x^22 + w*x^21 + w*x^19 + w^2*x^18 + w^2*x^16 + x^14 + x^13 + w*x^10 + x^8 + x^6 + x^5 + w*x^4 + w^2*x^3 + 1
[2]: [[85, 5, 19]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[84, 5, 18]] quantum code over GF(2^2)
Puncturing of [2] at { 85 }
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 1 1 0 0 1|0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[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 1 1 0 1 1|0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 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 1 0 0 1 1 0|1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1]
last modified: 2013-12-09
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