Bounds on the minimum distance of additive quantum codes

Bounds on [[71,38]]2

lower bound:8
upper bound:11

Construction

Construction of a [[71,38,8]] quantum code:
[1]:  [[70, 38, 8]] quantum code over GF(2^2)
     QuasiCyclicCode of length 70 stacked to height  2 with generating polynomials: x^21 + x^19 + w*x^18 + w^2*x^17 + w^2*x^16 + w*x^15 + x^14 + w^2*x^10 + x^9 + x^8 + w^2*x^7 + x^6 + w*x^5 + w*x^4 + w*x^2 + w^2*x + 1,  x^31 + w^2*x^30 + x^27 + x^26 + w^2*x^25 + x^24 + w*x^23 + w*x^22 + w*x^21 + w*x^19 + x^18 + x^17 + w^2*x^16 + w^2*x^13 + w^2*x^12 + w^2*x^11 + w^2*x^10 + x^9 + x^8 + x^6 + w^2*x^4 + w*x^2 + w^2*x,  0,  x^33 + w*x^32 + w*x^31 + x^30 + x^28 + w*x^27 + w*x^26 + x^25 + x^23 + w*x^22 + w*x^21 + x^20 + x^18 + w*x^17 + w*x^16 + x^15 + x^13 + w*x^12 + w*x^11 + x^10 + x^8 + w*x^7 + w*x^6 + x^5 + x^3 + w*x^2 + w*x + 1
[2]:  [[71, 38, 8]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    stabilizer matrix:

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

last modified: 2024-06-15

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024