Bounds on the minimum distance of additive quantum codes

Bounds on [[46,2]]2

lower bound:12
upper bound:16

Construction

Construction of a [[46,2,12]] quantum code:
[1]:  [[48, 0, 14]] self-dual Quantum code over GF(2^2)
     quasicyclic code of length 48 stacked to height 2 with 4 generating polynomials
[2]:  [[46, 2, 12]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 47, 48 }

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

last modified: 2006-04-07

Notes


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