Bounds on the minimum distance of additive quantum codes

Bounds on [[48,3]]2

lower bound:11
upper bound:16

Construction

Construction of a [[48,3,11]] 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]:  [[45, 3, 11]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 46, 47, 48 }
[3]:  [[48, 3, 11]] Quantum code over GF(2^2)
     ExtendCode [2] by 3

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

last modified: 2006-04-03

Notes


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