Bounds on the minimum distance of additive quantum codes
Bounds on [[74,0]]2
lower bound: | 18 |
upper bound: | 26 |
Construction
Construction of a [[74,0,18]] quantum code:
[1]: [[74, 0, 18]] self-dual quantum code over GF(2^2)
cyclic code of length 74 with generating polynomial w*x^73 + x^72 + w^2*x^71 + w*x^70 + w^2*x^69 + x^68 + x^67 + x^66 + x^64 + w*x^62 + x^61 + x^59 + w^2*x^58 + w*x^57 + w*x^56 + x^54 + w^2*x^52 + x^51 + x^49 + w^2*x^48 + w*x^41 + w*x^40 + w*x^39 + w*x^38 + w^2*x^37 + 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 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0]
[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 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1]
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last modified: 2008-02-11
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.
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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014