Bounds on the minimum distance of additive quantum codes
Bounds on [[87,0]]2
| lower bound: | 20 |
| upper bound: | 30 |
Construction
Construction type: Grassl
Construction of a [[87,0,20]] quantum code:
[1]: [[87, 0, 20]] self-dual quantum code over GF(2^2)
cyclic code of length 87 with generating polynomial x^81 + x^77 + x^76 + x^75 + x^74 + x^73 + x^68 + x^65 + x^64 + x^63 + x^61 + x^60 + x^59 + x^58 + x^57 + x^54 + x^53 + x^51 + x^48 + x^47 + x^46 + x^41 + x^40 + x^39 + x^36 + x^34 + x^33 + x^30 + x^29 + x^28 + x^27 + x^26 + x^24 + x^23 + x^22 + x^19 + x^14 + x^13 + x^12 + x^11 + x^10 + x^6 + 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 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 1 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 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]
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last modified: 2011-06-27
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 necessarily 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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