Bounds on the minimum distance of additive quantum codes

Bounds on [[63,16]]2

lower bound:11
upper bound:17

Construction

Construction of a [[63,16,11]] quantum code:
[1]:  [[63, 16, 11]] Quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomial w^2*x^62 + x^59 + w^2*x^58 + w*x^56 + x^55 + w^2*x^53 + x^52 + w^2*x^51 + w^2*x^49 + x^48 + w^2*x^47 + w^2*x^45 + w*x^44 + w*x^43 + w*x^41 + w*x^39 + x^38 + w^2*x^37 + w*x^36 + w^2*x^35 + w^2*x^32 + x^30 + x^23 + 1

    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 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1|0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 0 1 0 1|0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 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 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 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1|0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 0 1 0 0|0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 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 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 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0|0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 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 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 1 1 1 0 1 1 0 0 0 1 1 1 0 1|0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 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 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 1 1 1 0 1 1 1 1 0 1 1 1|0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 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 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 1 0 1 0 0 0 0 0 0 0 0 1 0|0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 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 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 1 0 1 0 0 0 0 0 0 0 0 1|0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 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 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 1 0 0 1 1 0 0 1 1 1 1 0 0 1|0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 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 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 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1|0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 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 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 1 0 0 1 1 0 1 0 1 1 0 1 1|0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 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 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 1 0 1 0 1 1 0 1 0 1 0 0|0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 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 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 1 0 1 0 1 1 0 1 0 1 0|0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 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 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 1 0 1 0 1 1 0 1 0 1|0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 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 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 1 1 1 0 0 0 1 0 0 0 1 1|0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 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 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 0 1 0 1 0 0 0 1 1 0 1 0 0 0|0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0]
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      [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 1 1 0 1 0 1 0 0 0 1 1 0 1 0|0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 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 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 0 1 0 1 0 0 0 1 1 0 1|1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 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 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 0 0 0 1 1 1 1 1 1|1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 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 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 0 0 0 1 1 0 0 1 1 0|0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 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 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 0 0 0 1 1 0 0 1 1|1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 0 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 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 1 0 0 1 0 0 0 1 1 0 0 0 0 0|0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 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 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 1 0 0 1 0 0 0 1 1 0 0 0 0|1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 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 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 1 0 0 1 0 0 0 1 1 0 0 0|0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 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 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 1 0 0 1 0 0 0 1 1 0 0|0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 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 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 1 0 0 1 0 0 0 1 1 0|1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 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 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 1 0 0 1 0 0 0 1 1|0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 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 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 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0|0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 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 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 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0|1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 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 1 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 1 1 1 0 1 0|1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1]
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last modified: 2008-02-16

Notes


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