Bounds on the minimum distance of additive quantum codes

Bounds on [[43,3]]2

lower bound:11
upper bound:14

Construction

Construction of a [[43,3,11]] quantum code:
[1]:  [[42, 3, 11]] Quantum code over GF(2^2)
     cyclic code of length 42 with generating polynomials [
w^2*x^41 + w^2*x^38 + x^35 + x^34 + x^32 + w^2*x^31 + x^30 + w*x^27 + w*x^26 + w^2*x^25 + w*x^24 + w*x^23 + w*x^22 + w^2*x^21 + w^2*x^20 + 1,
w^2*x^40 + x^39 + w*x^37 + w*x^36 + w^2*x^35 + w*x^33 + w*x^32 + w*x^29 + w*x^27 + w^2*x^26 + w^2*x^25 + w*x^23 + x^21 + w*x^20 + w*x^19 + w
]
[2]:  [[43, 3, 11]] Quantum code over GF(2^2)
     ExtendCode [1] by 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 0 0 0 0 1 1 0 1 1 0 1 1 0|0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0|0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 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 1 0 1 1 0 1 1 0|0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 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 1 1 1 1 0 1 1 0 0|0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0|0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 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 1 1 1 0 0 1 1 0 0|0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 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 1 1 1 0 0 1 1 0|0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 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 1 1 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 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 1 1 1 0 0 0 1 0|0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 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 0 0 0 0 0 1 1 1 0 0 0 1 1 0|0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 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 0 1 0 1 0 1 0 1 0 0|0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 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 0 1 0 1 0 1 0 1 0|0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 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 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 1 0 0 0 1 0|0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0|0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 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 1 0 0 0 1 0 1 0 0|0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0|0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 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 1 1 1 1 1 0 0 1 0|0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0|0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0|0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 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 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 0|0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 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 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|0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 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 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 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0|0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0|0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0|0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0|0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0|0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 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 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0|0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0|0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0|0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 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 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0|0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 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 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0|0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 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 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0|0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 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 1 1 0 1 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 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 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|1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 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 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 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 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 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 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 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 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 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 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 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 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0]

last modified: 2006-04-03

Notes


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