Bounds on the minimum distance of additive quantum codes

Bounds on [[256,166]]₂

Construction

Construction of a [[256,166,16]] quantum code:
[1]:  [[256, 166, 16]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 15

    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 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 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 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1]
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last modified: 2009-02-08

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.