Bounds on the minimum distance of additive quantum codes

Bounds on [[116,94]]2

lower bound:5
upper bound:6

Construction

Construction of a [[116,94,5]] quantum code:
[1]:  [[114, 96, 5]] quantum code over GF(2^2)
     QuasiCyclicCode of length 114 with generating polynomials: w*x^18 + w^2*x^17 + w^2*x^16 + x^14 + w*x^12 + w*x^11 + w^2*x^10 + x^9 + 1,  x^18 + x^17 + w*x^16 + x^15 + w^2*x^14 + x^13 + w^2*x^12 + w^2*x^11 + x^10 + w*x^9 + w*x^8 + w*x^6 + w*x^5 + x^4 + x^2 + w*x + w,  w*x^18 + w^2*x^17 + x^16 + x^15 + w^2*x^14 + x^13 + w^2*x^12 + w*x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + w*x^7 + w^2*x^6 + w^2*x^4 + w*x^3 + w*x^2 + w,  w^2*x^18 + x^17 + w*x^15 + w^2*x^13 + w*x^12 + w^2*x^9 + x^8 + w*x^6 + w*x^5 + x^4 + w*x^3 + w*x + w,  w^2*x^18 + w^2*x^17 + w*x^16 + x^15 + w*x^13 + w*x^12 + w*x^10 + x^9 + w*x^8 + x^7 + w^2*x^6 + w^2*x^3 + w^2*x^2 + x + 1,  w*x^18 + w^2*x^17 + w*x^16 + x^14 + x^13 + w*x^12 + x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + x^6 + w^2*x^5 + w*x^4 + w^2*x^3 + 1
[2]:  [[114, 94, 5]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[116, 94, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 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 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 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 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0|1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 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 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0|0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 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 0 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0|0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 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 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0|0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0]
      [0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 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 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0|0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 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 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 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 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 1 1 1 0 1 0 0 1 0 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 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0|0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0]
      [0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 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 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0|0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0]
      [0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 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 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0|0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 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 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 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 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0]
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last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014