Bounds on the minimum distance of additive quantum codes

Bounds on [[40,13]]2

lower bound:7
upper bound:10

Construction

Construction of a [[40,13,7]] quantum code:
[1]:  [[35, 13, 7]] Quantum code over GF(2^2)
     cyclic code of length 35 with generating polynomials [
x^34 + x^33 + w*x^32 + x^31 + x^30 + w^2*x^29 + w*x^27 + w*x^26 + x^25 + w^2*x^24 + w*x^23 + x^21 + w^2*x^20 + w*x^19 + w^2*x^18 + w^2*x^17 + w^2*x^15 + w*x^14 + w^2*x^13 + w^2*x^12 + x^11 + 1,
w*x^34 + w*x^33 + w^2*x^32 + w*x^31 + w*x^30 + x^29 + w^2*x^27 + w^2*x^26 + w*x^25 + x^24 + w^2*x^23 + w*x^21 + x^20 + w^2*x^19 + x^18 + x^17 + x^15 + w^2*x^14 + x^13 + x^12 + w*x^11 + w
]
[2]:  [[40, 13, 7]] Quantum code over GF(2^2)
     ExtendCode [1] by 5

    stabilizer matrix:

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