Bounds on the minimum distance of additive quantum codes

Bounds on [[23,2]]2

lower bound:7
upper bound:8

Construction

Construction of a [[23,2,7]] quantum code:
[1]:  [[24, 1, 8]] Quantum code over GF(2^2)
     cyclic code of length 24 with generating polynomial x^23 + w^2*x^22 + w*x^20 + w*x^18 + w*x^16 + x^15 + w*x^14 + w*x^13 + x^12 + x^11 + x
[2]:  [[23, 2, 7]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 24

    stabilizer matrix:

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

last modified: 2005-07-28

Notes


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