Bounds on the minimum distance of additive quantum codes
Bounds on [[83,0]]2
lower bound: | 20 |
upper bound: | 29 |
Construction
Construction of a [[83,0,20]] quantum code:
[1]: [[83, 0, 20]] self-dual quantum code over GF(2^2)
cyclic code of length 83 with generating polynomial x^81 + x^80 + x^79 + x^77 + x^75 + x^73 + x^70 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^57 + x^56 + x^54 + x^53 + x^52 + x^51 + x^50 + x^48 + x^46 + x^43 + x^40 + x^37 + x^35 + x^33 + x^32 + x^31 + x^30 + x^29 + x^27 + x^26 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^13 + x^10 + x^8 + x^6 + x^4 + x^3 + x^2 + w
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 1|0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 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 0 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
last modified: 2015-06-02
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