Bounds on the minimum distance of additive quantum codes

Bounds on [[88,43]]2

lower bound:10
upper bound:15

Construction

Construction of a [[88,43,10]] quantum code:
[1]:  [[85, 45, 9]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomials [
x^84 + w*x^83 + x^82 + w*x^81 + w*x^80 + x^79 + w*x^78 + x^75 + w*x^74 + w*x^71 + w*x^69 + x^68 + w*x^67 + w^2*x^66 + w^2*x^65 + x^64 + w^2*x^62 + x^61 + x^57 + w^2*x^56 + w*x^55 + x^54 + w^2*x^53 + w^2*x^51 + w*x^50 + w*x^49 + w*x^48 + w^2*x^47 + w^2*x^46 + x^45 + w^2*x^44 + w*x^43 + w*x^41 + x^40 + w^2*x^39 + x^38 + w^2*x^35 + x^34 + x^33 + w*x^29 + w^2*x^28 + w*x^27 + w^2*x^26 + w^2*x^25 + x^24 + x^23 + x^20 + 1,
w*x^84 + w^2*x^83 + w*x^82 + w^2*x^81 + w^2*x^80 + w*x^79 + w^2*x^78 + w*x^75 + w^2*x^74 + w^2*x^71 + w^2*x^69 + w*x^68 + w^2*x^67 + x^66 + x^65 + w*x^64 + x^62 + w*x^61 + w*x^57 + x^56 + w^2*x^55 + w*x^54 + x^53 + x^51 + w^2*x^50 + w^2*x^49 + w^2*x^48 + x^47 + x^46 + w*x^45 + x^44 + w^2*x^43 + w^2*x^41 + w*x^40 + x^39 + w*x^38 + x^35 + w*x^34 + w*x^33 + w^2*x^29 + x^28 + w^2*x^27 + x^26 + x^25 + w*x^24 + w*x^23 + w*x^20 + w
]
[2]:  [[86, 44, 10]] quantum code over GF(2^2)
     standard lengthening of  [1]
[3]:  [[86, 43, 10]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[88, 43, 10]] quantum code over GF(2^2)
     ExtendCode [3] by 2

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