Bounds on the minimum distance of additive quantum codes

Bounds on [[37,8]]2

lower bound:8
upper bound:11

Construction

Construction of a [[37,8,8]] quantum code:
[1]:  [[34, 8, 8]] quantum code over GF(2^2)
     cyclic code of length 34 with generating polynomial x^33 + w*x^32 + x^31 + w^2*x^28 + w^2*x^27 + w^2*x^25 + x^24 + w*x^23 + x^21 + w^2*x^19 + x^16 + w^2*x^13 + 1
[2]:  [[35, 8, 8]] quantum code over GF(2^2)
     ExtendCode [1] by 1
[3]:  [[37, 8, 8]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    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 1 1 1 0 1 0 1 1 0 0 0|0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 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 1 0 0 1 1 1 1 0 0 0 0|0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 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 1 0 0 1 1 1 1 0 0 0|1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 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 1 1 0 0 1 1 0 0 0 0 0|1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 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 1 1 0 0 1 1 0 0 0 0|0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 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 1 1 0 0 1 1 0 0 0|0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 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 1 1 1 1 0 0 1 0 0 0 0|1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 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 1 1 1 1 0 0 1 0 0 0|0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 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 1 1 0 1 0 1 1 1 0 0 0|0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0|1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0|1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0|0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0|0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0|1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0|1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 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 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 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 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 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 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0|1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0|0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0|0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 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 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0|1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 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 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0|0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 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 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0|1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 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 1 0 0 1 1 1 1 0 0 1 0 0 0 0|1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0|1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 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 1 1 1 0 1 0 1 1 1 0 0 0|0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 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 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 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 0 0 0 0 0 0 0 0 0 0 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: 2006-04-07

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014