Bounds on the minimum distance of additive quantum codes

Bounds on [[46,0]]2

lower bound:14
upper bound:16

Construction

Construction type: GulliverHarada

Construction of a [[46,0,14]] quantum code:
[1]:  [[46, 0, 14]] self-dual Quantum code over GF(2^2)
     quasicyclic code of length 46 stacked to height 2 with 4 generating polynomials

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

last modified: 2007-04-10

Notes


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