Bounds on the minimum distance of additive quantum codes

Bounds on [[253,164]]₂

Construction

Construction of a [[253,164,13]] quantum code:
[1]:  [[256, 166, 16]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 15
[2]:  [[253, 169, 13]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 254 .. 256 }
[3]:  [[253, 164, 13]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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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.