Bounds on the minimum distance of additive quantum codes

Bounds on [[82,42]]₂

lower bound:	9
upper bound:	13
Construction

Construction type: EzermanGrasslLingOzbudakOzkaya
Construction of a [[82,42,9]] quantum code:
[1]:  [[82, 42, 9]] quantum code over GF(2^2)
     QuasiTwistedCyclicCode of length 82 and constant w with generators: x^21 + x^20 + w^2*x^19 + w*x^17 + w^2*x^16 + w*x^15 + w^2*x^14 + w^2*x^11 + w*x^10 + w*x^7 + w*x^6 + x^5 + x^4 + x^2 + w^2*x + 1,  x^40 + x^39 + w^2*x^38 + w^2*x^37 + w*x^36 + x^35 + w*x^33 + w^2*x^32 + w^2*x^31 + w^2*x^30 + w^2*x^29 + w^2*x^28 + w*x^27 + x^26 + w*x^23 + w*x^22 + w*x^21 + w^2*x^20 + w*x^17 + w*x^16 + w^2*x^15 + w*x^14 + x^11 + w*x^8 + w^2*x^5 + w^2*x^4 + w^2*x^3 + w*x^2 + w^2*x + w^2

    stabilizer matrix:

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

last modified: 2024-06-07
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 [[82,42]]2

Construction

Notes

Bounds on [[82,42]]₂
