Bounds on the minimum distance of additive quantum codes

Bounds on [[63,33]]2

lower bound:7
upper bound:10

Construction

Construction type: BE

Construction of a [[63,33,7]] quantum code:
[1]:  [[63, 33, 7]] Quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomials [
w*x^62 + w^2*x^61 + w*x^60 + w*x^59 + w*x^58 + w*x^55 + w*x^53 + w^2*x^52 + w^2*x^50 + w*x^49 + x^48 + x^47 + w^2*x^46 + w*x^45 + w*x^44 + w^2*x^43 + w^2*x^42 + x^41 + w*x^40 + w*x^39 + x^37 + x^36 + x^35 + w*x^34 + x^33 + w^2*x^32 + w*x^31 + w*x^30 + w*x^29 + x^27 + x^26 + x^25 + w^2*x^24 + w^2*x^23 + x^21 + w^2*x^20 + w^2*x^18 + w*x^17 + w^2*x^15 + 1,
w^2*x^62 + x^61 + w^2*x^60 + w^2*x^59 + w^2*x^58 + w^2*x^55 + w^2*x^53 + x^52 + x^50 + w^2*x^49 + w*x^48 + w*x^47 + x^46 + w^2*x^45 + w^2*x^44 + x^43 + x^42 + w*x^41 + w^2*x^40 + w^2*x^39 + w*x^37 + w*x^36 + w*x^35 + w^2*x^34 + w*x^33 + x^32 + w^2*x^31 + w^2*x^30 + w^2*x^29 + w*x^27 + w*x^26 + w*x^25 + x^24 + x^23 + w*x^21 + x^20 + x^18 + w^2*x^17 + x^15 + w
]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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