Bounds on the minimum distance of additive quantum codes

Bounds on [[63,35]]₂

lower bound:	7
upper bound:	10
Construction

Construction of a [[63,35,7]] quantum code:
[1]:  [[63, 35, 7]] quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomial x^61 + x^60 + x^59 + x^57 + w^2*x^56 + x^55 + x^54 + w*x^51 + x^50 + w^2*x^48 + w*x^47 + x^44 + w*x^43 + w*x^42 + w^2*x^40 + x^39 + w^2*x^38 + w*x^36 + w^2*x^34 + x^33 + w^2*x^29 + w*x^27 + w^2*x^26 + w^2*x^25 + x^24 + w^2*x^23 + w*x^22 + w*x^21 + x^18 + w^2*x^17 + w*x^16 + w*x^14 + 1

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

last modified: 2008-02-18
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.
This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014
Bounds on the minimum distance of additive quantum codes

Bounds on [[63,35]]2

Construction

Notes

Bounds on [[63,35]]₂
