Bounds on the minimum distance of additive quantum codes

Bounds on [[44,30]]2

lower bound:4
upper bound:5

Construction

Construction of a [[44,30,4]] quantum code:
[1]:  [[40, 30, 4]] quantum code over GF(2^2)
     QuasiCyclicCode of length 40 stacked to height 2 with generating polynomials: 1,  w^2*x^4 + w*x^3 + w^2*x^2 + w*x + w^2,  x^4 + w^2*x^2 + w^2*x + w^2,  x^4 + w*x^3 + x^2,  w*x^4 + x^3 + w^2*x,  w*x^4 + x^3 + x^2 + x,  w^2*x^4 + x^2 + w*x,  x^4 + w^2*x^3 + w^2*x^2 + x + 1,  w,  x^4 + w^2*x^3 + x^2 + w^2*x + 1,  w*x^4 + x^2 + x + 1,  w*x^4 + w^2*x^3 + w*x^2,  w^2*x^4 + w*x^3 + x,  w^2*x^4 + w*x^3 + w*x^2 + w*x,  x^4 + w*x^2 + w^2*x,  w*x^4 + x^3 + x^2 + w*x + w
[2]:  [[44, 30, 4]] quantum code over GF(2^2)
     ExtendCode [1] by 4

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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