Bounds on the minimum distance of additive quantum codes

Bounds on [[77,41]]₂

lower bound:	8
upper bound:	12
Construction

Construction of a [[77,41,8]] quantum code:
[1]:  [[78, 40, 9]] quantum code over GF(2^2)
     QuasiCyclicCode of length 78 with generating polynomials: x^20 + x^19 + x^18 + w*x^17 + w*x^16 + w*x^15 + x^14 + x^13 + w*x^12 + w*x^11 + w*x^10 + w^2*x^8 + x^7 + w*x^4 + x^2 + w*x + w,  x^37 + w^2*x^36 + w*x^35 + w^2*x^34 + x^32 + x^31 + w*x^30 + x^29 + x^28 + x^27 + w^2*x^26 + w*x^25 + w^2*x^24 + w*x^23 + w*x^22 + w*x^20 + w^2*x^19 + x^17 + w*x^16 + w*x^15 + x^14 + w^2*x^13 + w^2*x^12 + w*x^11 + w*x^9 + x^8 + x^6 + w^2*x^5 + w^2*x^4 + w*x^2 + x
[2]:  [[77, 41, 8]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 78 }

    stabilizer matrix:

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

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 [[77,41]]2

Construction

Notes

Bounds on [[77,41]]₂
