Bounds on the minimum distance of additive quantum codes

Bounds on [[47,0]]2

lower bound:13
upper bound:17

Construction

Construction of a [[47,0,13]] quantum code:
[1]:  [[48, 0, 14]] self-dual Quantum code over GF(2^2)
     cyclic code of length 48 with generating polynomial w*x^47 + w^2*x^44 + w^2*x^43 + x^42 + w^2*x^40 + w^2*x^39 + x^38 + w^2*x^37 + x^35 + w^2*x^34 + x^31 + w^2*x^30 + w^2*x^29 + w*x^27 + w*x^25 + w*x^24 + w*x^23 + 1
[2]:  [[47, 1]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 48
[3]:  [[47, 0, 13]] self-dual Quantum code over GF(2^2)
     Subcode of [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 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 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 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 0 1 0 0 0 0 0 0 0 0|1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0|0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0|0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 1 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 0 0 0|1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0|1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0|0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 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 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 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 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 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 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 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 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|1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 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 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 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 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 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 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 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 1 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 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 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 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 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 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 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 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 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 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 0 0 0|1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 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 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 0 0 0 0 0 0|0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 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 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 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 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 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 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 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 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 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 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 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0|1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0|0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0|0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 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 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 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 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 0 0 0 0 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 0 0 0 0 0 0|1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 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 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 1 0 0 0 0 0 0 0 0|0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 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]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0|0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 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 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 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 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 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 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0]

last modified: 2009-02-08

Notes


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