Bounds on the minimum distance of additive quantum codes

Bounds on [[34,7]]2

lower bound:8
upper bound:10

Construction

Construction of a [[34,7,8]] 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]:  [[34, 7, 8]] quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024