Bounds on the minimum distance of additive quantum codes

Bounds on [[45,0]]2

lower bound:13
upper bound:16

Construction

Construction type: Gra

Construction of a [[45,0,13]] quantum code:
[1]:  [[45, 0, 13]] self-dual Quantum code over GF(2^2)
     cyclic code of length 45 with generating polynomial x^44 + x^43 + w^2*x^41 + w^2*x^40 + x^39 + x^38 + w*x^37 + w*x^36 + w^2*x^35 + w*x^33 + w^2*x^32 + w*x^30 + x^27 + w^2*x^26 + w^2*x^25 + w*x^24 + w*x^23 + w*x^21 + w*x

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

last modified: 2006-04-17

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014