Bounds on the minimum distance of additive quantum codes

Bounds on [[16,15]]₂

Construction

Construction of a [[16,15,1]] quantum code:
[1]:  [[15, 15, 1]] quantum code over GF(2^2)
     UniverseCode of length 15
[2]:  [[16, 15, 1]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    stabilizer matrix:

      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

last modified: 2005-06-27

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 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.