Bounds on the minimum distance of additive quantum codes

Bounds on [[63,31]]₂

lower bound:	8
upper bound:	11
Construction

Construction type: GuanLiLuYao
Construction of a [[63,31,8]] quantum code:
[1]:  [[63, 31, 8]] quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomial w^2*x^60 + w*x^59 + w*x^58 + x^57 + x^56 + w*x^55 + w*x^53 + x^51 + x^49 + w*x^46 + w^2*x^45 + x^43 + w^2*x^42 + w^2*x^39 + x^37 + w^2*x^36 + x^34 + x^33 + w^2*x^32 + x^31 + w^2*x^30 + x^29 + w*x^28 + w^2*x^27 + w^2*x^25 + w*x^24 + x^23 + x^21 + w^2*x^19 + w*x^17 + w*x^15 + w*x^12

    stabilizer matrix:

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

last modified: 2022-08-02
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.
This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024
Bounds on the minimum distance of additive quantum codes

Bounds on [[63,31]]2

Construction

Notes

Bounds on [[63,31]]₂
