Bounds on the minimum distance of additive quantum codes
Bounds on [[83,14]]2
lower bound: | 15 |
upper bound: | 24 |
Construction
Construction of a [[83,14,15]] quantum code:
[1]: [[85, 13, 17]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomial x^36 + w*x^35 + w*x^34 + w^2*x^33 + w*x^32 + w^2*x^30 + w^2*x^29 + w*x^28 + x^27 + w*x^25 + x^23 + w^2*x^21 + w*x^20 + x^19 + w^2*x^18 + w*x^17 + w*x^15 + w*x^13 + x^12 + w*x^11 + w^2*x^10 + w*x^8 + w*x^7 + x^6 + w^2*x^5 + x^4 + w^2*x^3 + x + 1
[2]: [[83, 15, 15]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at { 84 .. 85 }
[3]: [[83, 14, 15]] 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 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1]
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last modified: 2015-05-28
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