Bounds on the minimum distance of additive quantum codes

Bounds on [[61,22]]2

lower bound:9
upper bound:14

Construction

Construction of a [[61,22,9]] quantum code:
[1]:  [[62, 22, 10]] quantum code over GF(2^2)
     QuasiTwistedCyclicCode of length 62 and constant w^2 with generators: x^11 + x^8 + w^2*x^7 + x^5 + w^2*x^4 + w,  x^30 + x^27 + w^2*x^24 + w*x^22 + w*x^21 + w*x^19 + w^2*x^18 + w^2*x^17 + x^16 + w*x^15 + x^14 + w^2*x^13 + w^2*x^12 + w^2*x^11 + w^2*x^10 + w^2*x^9 + w*x^7 + w*x^6 + w*x^5 + w*x^2 + w*x + w^2
[2]:  [[61, 22, 9]] quantum code over GF(2^2)
     Puncturing of [1] at { 62 }

    stabilizer matrix:

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

last modified: 2024-06-08

Notes


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