Bounds on the minimum distance of additive quantum codes

Bounds on [[56,4]]₂

lower bound:	13
upper bound:	18
Construction

Construction of a [[56,4,13]] quantum code:
[1]:  [[57, 3, 14]] quantum code over GF(2^2)
     cyclic code of length 57 with generating polynomial w^2*x^56 + x^55 + x^54 + x^53 + w^2*x^52 + w^2*x^51 + w*x^50 + w*x^49 + x^48 + x^47 + w^2*x^46 + x^45 + w*x^44 + w^2*x^42 + w^2*x^41 + w*x^40 + w^2*x^39 + w*x^37 + w^2*x^36 + x^35 + x^33 + x^31 + x^29 + x^27 + w^2*x^26 + w*x^23 + w*x^22 + w^2*x^21 + x^20 + x^19 + w^2*x^18 + w*x^16 + x^15 + w^2*x^13 + w*x^12 + w^2*x^11 + x^9 + w*x^7 + w^2*x^6 + x^4 + w^2*x^3 + w^2*x^2 + w^2*x + w^2
[2]:  [[56, 4, 13]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 57 }

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

last modified: 2022-08-07
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 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 [[56,4]]2

Construction

Notes

Bounds on [[56,4]]₂
