Bounds on the minimum distance of additive quantum codes

Bounds on [[58,23]]2

lower bound:8
upper bound:12

Construction

Construction of a [[58,23,8]] quantum code:
[1]:  [[58, 28, 8]] quantum code over GF(2^2)
     quasicyclic code of length 58 stacked to height 2 with 4 generating polynomials
[2]:  [[58, 23, 8]] quantum code over GF(2^2)
     Subcode of [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 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1|0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 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 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0|0 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 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 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1|0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1|0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 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 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1|0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 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 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1|0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 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 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1|0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 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 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0|0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 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 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1|0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 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 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0|0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 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 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1|0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 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 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1|0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 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 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0|0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 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 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0|0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 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 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0|0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 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 0 1 0 0 0 1 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 0 0 0 0 0 0 0 1 1 1 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 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 1 1 1 1 0 0 0 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0|0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0|0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 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 0 0 1 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 0 0 1 1 0 1 0 0 0 1 0 1|0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 1 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 1 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 0 1 1 1 1 1 1|0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0|0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1|0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 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 1 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 1 1 1 0 0 1 1 1|0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0|0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1|0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1|0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 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 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0|0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1|0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1|0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 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 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0|0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 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 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 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 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 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 1 1 0 0 1 0 0 1 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 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 1 1 1 1 1 1 1 1 1 1 1 1]

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014