Bounds on the minimum distance of additive quantum codes

Bounds on [[76,35]]₂

lower bound:	8
upper bound:	14
Construction

Construction of a [[76,35,8]] quantum code:
[1]:  [[74, 38, 8]] quantum code over GF(2^2)
     QuasiCyclicCode of length 74 with generating polynomials: w^2*x^34 + w^2*x^31 + w^2*x^30 + w*x^29 + x^27 + x^26 + w*x^25 + w^2*x^24 + w*x^23 + x^22 + w^2*x^21 + w*x^20 + w^2*x^19 + w*x^18 + w^2*x^17 + x^16 + w*x^14 + x^13 + w^2*x^12 + w^2*x^10 + w*x^9 + x^8 + w^2*x^5 + w^2*x^2 + w^2*x + w,  x^36 + w*x^35 + x^32 + x^31 + x^30 + w*x^27 + w*x^26 + w^2*x^25 + x^24 + w^2*x^23 + x^21 + w*x^20 + x^19 + w*x^18 + w^2*x^17 + w*x^15 + w*x^13 + w*x^12 + w^2*x^11 + x^10 + x^8 + w^2*x^6 + w^2*x^4 + x^2 + w^2*x + w^2
[2]:  [[74, 35, 8]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[76, 35, 8]] quantum code over GF(2^2)
     ExtendCode [2] by 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 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 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 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 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 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 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 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 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 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 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 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 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 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 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 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 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 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 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 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 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 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 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 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 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 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 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 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 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 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 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 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 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 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 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 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 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 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 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 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 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 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 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 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 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 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 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 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 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 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 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 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 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 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 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 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 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 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 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 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 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 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 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 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 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 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 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 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 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 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 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 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 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 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 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 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 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 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 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 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 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 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 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 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 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 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 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 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 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 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 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 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 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 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 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 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 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 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 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 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 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 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 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 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 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 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 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 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 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 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 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 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 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 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 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 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 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 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 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 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 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 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 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 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 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 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 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 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 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 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 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 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 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 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 1 1 0 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 0 0 0 0 0 0 0 0 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 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 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 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 1 0 0 1 1 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 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 1 1 1 0 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]

last modified: 2006-04-03
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 [[76,35]]2

Construction

Notes

Bounds on [[76,35]]₂
