Bounds on the minimum distance of additive quantum codes

Bounds on [[45,16]]2

lower bound:8
upper bound:11

Construction

Construction type: GuanLiLuYao

Construction of a [[45,16,8]] quantum code:
[1]:  [[45, 16, 8]] quantum code over GF(2^2)
     cyclic code of length 45 with generating polynomial x^44 + x^43 + x^42 + x^41 + x^40 + w*x^39 + w*x^38 + w^2*x^36 + w*x^35 + w*x^34 + w*x^33 + x^32 + w^2*x^30 + w*x^29 + x^28 + x^27 + w*x^26 + w^2*x^25 + w*x^23 + w^2*x^22 + w^2*x^21 + w*x^17 + w^2*x^14

    stabilizer matrix:

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

last modified: 2022-08-02

Notes


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