Bounds on the minimum distance of additive quantum codes

Bounds on [[29,6]]2

lower bound:7
upper bound:9

Construction

Construction of a [[29,6,7]] quantum code:
[1]:  [[30, 5, 8]] Quantum code over GF(2^2)
     cyclic code of length 30 with generating polynomial w^2*x^29 + x^28 + w*x^26 + w*x^25 + w*x^24 + w*x^23 + w^2*x^22 + w*x^21 + w*x^20 + w*x^18 + w^2*x^17 + x^16 + w^2*x^14 + x^13 + w*x^12 + 1
[2]:  [[29, 6, 7]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 30

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

last modified: 2005-08-08

Notes


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