Bounds on the minimum distance of additive quantum codes
Bounds on [[111,3]]2
| lower bound: | 25 |
| upper bound: | 37 |
Construction
Construction type: DastbastehPadashnickCrespoGrasslSharafi
Construction of a [[111,3,25]] quantum code:
[1]: [[111, 3, 25]] quantum code over GF(2^2)
constacyclic code generated by x^54 + w^2*x^53 + x^52 + x^51 + x^50 + w*x^49 + w^2*x^48 + w^2*x^47 + w*x^46 + x^45 + w^2*x^43 + x^42 + w^2*x^40 + w*x^37 + x^36 + x^35 + w^2*x^31 + x^28 + x^27 + w*x^25 + x^24 + x^23 + w^2*x^20 + w*x^19 + w^2*x^17 + w^2*x^16 + x^14 + w*x^13 + w^2*x^11 + x^10 + w^2*x^7 + w^2*x^3 + w*x^2 + w*x + 1 with shift constant 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 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 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 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1]
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last modified: 2024-05-08
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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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024