Bounds on the minimum distance of additive quantum codes

Bounds on [[161,1]]₂

Construction

Construction of a [[161,1,33]] quantum code:
[1]:  [[5, 1, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[29, 1, 11]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[3]:  [[145, 1, 33]] quantum code over GF(2^2)
     Concatenation of [2] and [1]
[4]:  [[161, 1, 33]] quantum code over GF(2^2)
     ExtendCode [3] by 16

    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.