Bounds on the minimum distance of additive quantum codes

Bounds on [[79,22]]₂

lower bound:	12
upper bound:	20
Construction

Construction of a [[79,22,12]] quantum code:
[1]:  [[78, 25, 12]] quantum code over GF(2^2)
     cyclic code of length 78 with generating polynomial x^55 + x^52 + w^2*x^51 + w^2*x^50 + x^49 + w^2*x^47 + w*x^46 + x^45 + w^2*x^44 + w*x^43 + x^42 + x^41 + w*x^40 + w^2*x^39 + w^2*x^38 + x^37 + w^2*x^36 + w^2*x^35 + w^2*x^33 + w^2*x^32 + w*x^31 + w*x^30 + w^2*x^29 + w^2*x^28 + w*x^27 + x^26 + w^2*x^25 + w*x^23 + w^2*x^22 + w^2*x^19 + w*x^18 + w^2*x^17 + w^2*x^16 + x^15 + x^14 + w*x^13 + w^2*x^12 + x^11 + w*x^10 + x^9 + x^8 + w*x^7 + w*x^6 + x^4 + x^2 + 1
[2]:  [[78, 22, 12]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[79, 22, 12]] quantum code over GF(2^2)
     ExtendCode [2] by 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 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 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 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 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 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 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 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 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 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 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 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 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 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 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 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 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 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 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 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 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 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 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 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 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 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 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 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 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 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 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 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 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 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 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 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 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 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 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 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 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 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 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 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 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 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 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 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 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 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 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 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 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 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 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 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 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 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 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 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 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 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 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 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 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 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 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 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 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 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 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 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 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 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 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 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 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 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 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 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 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 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 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 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 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 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 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 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 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 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 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 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 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 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 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 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 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 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 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 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 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 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 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 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 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 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 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 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 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 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 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 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 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 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 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 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 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 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 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 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 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 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 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 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 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 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 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 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

last modified: 2024-06-17
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 [[79,22]]2

Construction

Notes

Bounds on [[79,22]]₂
